Forensic Accounting

Forensic Accounting Introduction A Forensic accountant assists an organization in unraveling issues surrounding financial problems. Mostly, his/her role involves analyzing financial information with the aim of unearthing fraud.Advertising We will write a custom research paper sample on Forensic Accounting specifically for you for only $16.05 $11/page Learn More After analyzing financial information, a forensic accountant is required to summarise and give a detailed report of his/her findings to the responsible party for implementation. Moreover, a forensic accountant keeps records of all the evidence gathered during his/her forensic investigation. This enables a party in a dispute to review and make decisions. Furthermore, the report lays the ground for in-court settlement if the parties fail to arbitrate among them. Thus, a forensic accountant helps organizations to avert fraudulent financial activities and institute appropriate controls aimed at preventing future frauds. Impo rtant skills for a Forensic Accountant A person seeking to be a forensic accountant should possess some essential skills to enable him/her to carry the job more efficiently. Analytical skills are one of the key skills demanded in this job. Carlino (2010) points out that analytical skills involve having the capacity to tie data and knowledge gathered from different areas together to come up with a clear interpretation. This plays a key role in enhancing the accuracy of financial information gathered and simplifies decision making during the judgment process.Advertising Looking for research paper on accounting? Let's see if we can help you! Get your first paper with 15% OFF Learn More Moreover, Carlino (2010) cites that analytical skills help an individual to identify strengths, opportunities, weaknesses and articulate principles strategically as they relate to financial matters. Also, a forensic accountant should be a person possessing persistence skills. Inve stigations involving financial statements take many hours or days to study and analyze to detect if the questionable adjustment has been made. Having persistence skills helps an individual to spot other details which might have been skipped during the investigation. Davis et al. (2010) explain that a forensic accountant, after carrying out investigations, he/she writes reports and acts as a witness in the court. Thus, he/she has to possess effective communication skills to articulate what is contained in the report. Furthermore, accounting involves analyzing complex financial transactions, statements, and account details; after analyzing, an individual has to submit the findings either orally or in a written report. Thus, effective communication skills are important in presenting a clear report to enable people with no or limited accounting knowledge to understand. A forensic accountant should be a conscious stickler to detail. This skill is important when the accountant is sifting through massive financial information (Kay and Gierlasinski, 2001). Being conscious of details provides an individual with new insight and can lead to uncovering new evidence that might lead to a sustained prosecution in the court.Advertising We will write a custom research paper sample on Forensic Accounting specifically for you for only $16.05 $11/page Learn More Davis et al. (2010) point out that a strong background in accounting is important in pursuing a career in forensic accounting. A bachelors degree in accounting or related discipline is a requisite. Also, membership to a certified professional body and experience are mandatory. However, individuals may gain forensic accounting skills on the job. Forensic Accountant and the Courtroom Environment When an organization suspects financial misappropriation in the organization, it deploys forensic investigators to begin determining the magnitude, and the nature of the fraud. The forensic role, in this ca se, is to come up with findings to enable the court to take further actions against the culprits. In the courts, a forensic accountant unravels the evidence linked to financial fraud by testifying. Thus, as mentioned earlier, testifying needs efficient skills in communication because the forensic accountant has to cross-examine the parties involved in the fraud. A forensic accountant acts as a detective in the court environment. For instance, he/she has to interview the people involved in the fraud and extract more information necessary to sustain a case. Legal Responsibility of a Forensic accountant in the Business In most cases, a forensic accountant is hired by organizations and law professionals among others to help unravel financial crimes and offer litigation support services. According to Kay and Gierlasinski (2001), the society bestows a big responsibility to a forensic accountant; he/she has to detect, prevent, investigate high profiled white collar frauds; computer scams, terrorist funding and, among others, forms of financial crimes.Advertising Looking for research paper on accounting? Let's see if we can help you! Get your first paper with 15% OFF Learn More In his/her line of duty, a forensic accountant helps to protect the economic security of the business by working hand in hand with the law enforcers. How does a forensic accountant achieve this in practice? Dark and Leauanae (2004) explain that a forensic accountant detects the organization financial losses in advance; this practice has made many organizations save money which would have been otherwise embezzled. The timely prevention of fraud has built the trust of investors as it motivates them to continue investing their funds in the business. Also, Kay and Gierlasinski (2001) show that the field of forensic accounting provides job security for many forensic accountants. Many organizations are springing up and coupled with rising financial frauds; the need for financial accountants is increasing. Dark and Leauanae (2004) indicate that in the U.S., the field of forensic accounting has fixed thousands of jobs that were not feasible before. This has secured the economy because more people can earn a living by being forensic accountants. A forensic accountant analyses financial statements and evidence used in legal matters. Thus, the evidence uncovered is used to identify fraudulent activities such as insurance fraud, money laundering, tax evasion and other embezzlements in organizations. Besides, the forensic services are significant in uncovering the activities of drug trafficking and hidden assets of couples entangled in divorce matters. A forensic accountant gathers and analyses financial data using mathematical and investigative skills. The findings arrived are used as evidence in a court of law to apprehend the culprits. Moreover, a forensic accountant has to support the evidence produced in the court. This is to enable the court to make a concise legal decision against a financial criminal. Cases of Forensic Accounting Case 1: A shareholder’s dilemma A 73-year-old father had just made a comeback to his construction company after the board handed h im the presidency (Barrett, 2013). Barely two years in the office, he realized that the former president, his 42-year-old son, had devised various schemes to defraud the company. Nevertheless, to say, the son had already misappropriated a sum of $11 million of his fathers 55% shares of the company while he was in the office. Moreover, he had allocated about $6 million a year (for his father’s retirement) and a further $6,500 monthly stipend to the ex-wife of the father (Barrett, 2013). Role of Forensic Accountant The forensic investigators were invited to carry out a thorough forensic audit on the deposed son. The forensic audit was divided into two parts: to validate the assertions of misfeasance by the father, prior and after his return, and to demonstrate that during the son’s tenure, there was no misappropriation of funds the father had purported in the lawsuit. Besides, the forensic accountants were also mandated to carry out the valuation of the business to certi fy the son had not run the company into bankruptcy. Results The evidence gathered by the forensic accountants was presented to the legal consultants of the father and was admitted without argument. The evidence laid a basis for the legal proceedings and as a review for tightening the internal controls of the company. Case 2: The Smoking Gun (Internal Coup) A medical company was preparing to make an initial public offer (IPO), and the prerequisites such as the patient appointments had gone well with doctors in several Southeastern states in the U.S. Besides, the products on offer had been tasted and ascertained to be of high quality and ready for the IPO unveiling (Barrett, 2013). However, to sabotage the process, two corporate officers and deep-pocket investors had devised a strategy to remove the financial and operating staff and replace them with others who could easily be compromised. Moreover, to complicate the process, the deep-pocket investors suppressed the release of funds u nless the officers were sacked or replaced (Barrett, 2013). The attorney of the Chief Executive Officer had no substantial evidence on the conspiracy among the three; hence, a forensic audit was needed. Role of Financial Accountant The financial accountants were invited to ascertain whether there was a conspiracy between the three groups mentioned. They were tasked with analyzing the company’s hard drive and the laptops used by the two doctors under investigation. Results After conducting a thorough forensic examination in the victims’ offices and the company’s server, there was no evidence linking the three to conspiracy. However, further investigation revealed that the three indeed communicated through personal emails hosted by Hotmail and Yahoo, but not the companys official emails, running through the company’s server. Reference List Barrett, W. C. (2013). My Life in Crime: Chronicles of a Forensic Accountant. Web. Carlino, B. (2010). Forensic Skills in High Demand. Web. Davis, C., Ogilby, S., Farrell, R. (2010). Survival of the Analytically Fit: The DNA of an Effective Forensic Accountant. Web. Derk, G. R. Leauanae J. L. (2004). Expert witness qualifications and selection, Journal of Financial Crime, 12 (2), 165 171. Kay, C.C. Gierlasinski, N. J. (2001). Forensic accounting skills: will supply finally catch up to demand?, Managerial Auditing Journal, 16(6), 378 – 382. Forensic Accounting The increase of the percentage related to the financial and corporate crimes influences the changes in the role of forensic accounting for businesses. Specific forensic accounting skills are necessary to control the situation within companies in order to avoid and predict financial crimes because of the spread of financial fraud as the negative tendency in business.Advertising We will write a custom essay sample on Forensic Accounting specifically for you for only $16.05 $11/page Learn More From this point, forensic accountants are professionals who are responsible for determining frauds and for predicting financial crimes or for resolving the problematic situations when it is necessary to investigate the definite financial case. As a result, there is a range of skills which forensic accountants should possess as well as a set of responsibilities associated with the legal context of the work of a forensic accountant. That is why, it is important to focus on the most important skills necessary for realizing the internal control within the company in relation to financial issues and to determine the legal responsibility of forensic accountants when they investigate the cases in companies or discuss them in the courtroom. The Forensic Accountants’ Most Important Skills Forensic accountants should be skillful investigators in order to discuss the case in detail and find the problem as well as its causes. Furthermore, this kind of internal control is almost impossible without the effective auditing techniques used by forensic accountants in order to resolve the problems and focus on the financial frauds. According to Davis, Farrell, and Ogilby, to discover and explore the evidences associated with fraud activities and misrepresentation, a successful forensic accountant needs to have such developed skills as the analytical thinking, the orientation on details and facts, effective communication skills, the ability to analyze and interp ret the information, and auditing skills (Davis, Farrell, Ogilby, 2009). The concentration on these five skills allows forensic accountants’ effective performance and investigation activity. Analytical skills are important to help forensic accountants explore the case aspects and analyze them effectively in order to provide the report on the fact of frauds and financial crimes. Forensic accountants receive the access to the financial records of the company, and their task is to interpret and analyze this information with references to their analytical skills (Crumbley, Heitger, Smith, 2007). Thus, the orientation on details and facts is important because this is a path to determining the problem and solution to it. The next significant factor is effective oral communication which is necessary to find the information and examine the details of the case with the help of employees and managers as the subjects (Skalak, Golden, Clayton, 2011). Forensic accountants work directly with financial records and reports that is why auditing skills are extremely necessary to perform the basic duties of an accountant and controller of the company’s financial activities.Advertising Looking for essay on accounting? Let's see if we can help you! Get your first paper with 15% OFF Learn More The Role of a Forensic Accountant in a Courtroom Working with such cases as bankruptcy, personal injury claims, and corporate crimes, forensic accountants often perform in a courtroom as witnesses in relation to those cases on which the financial investigation is necessary. If the case is discussed in the courtroom, the role of a forensic accountant is to provide the necessary evidences based on the investigative activities which were realized to determine frauds and problems in the company (Pagano Buckhoff, 2005). Forensic accountants can be discussed as experts in the cases of financial and corporate crimes because of their focus on investigation an d analysis of the internal information, and this role of witnesses and experts can be used in the courtroom, depending on the case. The Legal Responsibility of a Forensic Accountant Forensic accountants are responsible for examining and analyzing a lot of cases and issues associated with business, depending on the needs of the company at the moment. Moreover, these responsibilities can be discussed as legal because forensic accountants must release any information about frauds and financial crimes which is discovered during the investigation without references to the company’s progress and status. From this perspective, forensic accountants’ legal responsibility is closely associated with the concepts of objectivity and justice (Bressler, 2010). The role of forensic accountants is important in business because their participation in investigation should guarantee the transparency of information and the legal approach to resolving the problem. Forensic Accounting Cases The cases of Enron and WorldCom are two situations when forensic accountants provided the vital evidences in order to resolve the legal questions and uncover the fact of crimes. During the development of Enron scandal in 2001, it was found that the company’s managers hided the information about the company’s financial situation and provided shareholders with the false reports in order to attract more investments and cover the company’s bankruptcy. The price of shares increased irrelevantly to the real situation within Enron. The collapse of Enron is closely connected with auditing and investigative activities realized by forensic accountants in order to examine the case in detail when the fraud was discussed as the fact. Focusing on Enron case, it is important to state that the significant role of forensic accountants is based on their investigation and found evidences which were presented in the courtroom. These evidences are necessary to prove the guilt of man agers responsible for the collapse. The case of WorldCom reflects the similar situation when managers of the company hided the information about the real earnings and profits in order to realize their fraud activities and avoid bankruptcy. The non-reported sums of money were used to conceal shortages in revenues within the company. Forensic accountants were responsible for investigating the case during a long period of time to present the most objective reports in the courtroom.Advertising We will write a custom essay sample on Forensic Accounting specifically for you for only $16.05 $11/page Learn More This situation affected the development of the opinion that forensic accountants should work with agencies as experts permanently in order to discover and prevent corporate and financial crimes and regulate the activities within the business world. The reflection of Enron situation in the case of WorldCom in 2002 emphasized the role of forensic accountants i n the process of auditing and interpreting financial reports and records (Crumbley, Heitger, Smith, 2007; Pagano Buckhoff, 2005). Thus, importance of forensic accountants in business is stated today as the well-known and admitted idea because the roles performed by forensic accountants allow the positive and fair progress of companies with references to the ethical principles and legal norms. From this perspective, forensic accountants can be discussed as protectors of the companies and the business community’s interests and in relation to guaranteeing the fair business relations. They also provide the appropriate discussion and resolution of such cases as commercial damages and personal injury claims which are also examined by forensic accountants because of the involvement of legal and financial aspects. References Bressler, L. (2010). The role of forensic accountants in fraud investigations: Importance of attorney and judge’s perceptions. Web. Crumbley, D. L., Hei tger, L. E., Smith, G. S. (2007). Forensic and investigative accounting. London: CCH. Davis, C., Farrell, R., Ogilby, S. (2009). Characteristics and skills of the forensic accountant. Web. Pagano, W., Buckhoff, T. (2005). Expert witnessing in forensic accounting. R.T. Edwards, Inc.Advertising Looking for essay on accounting? Let's see if we can help you! Get your first paper with 15% OFF Learn More Skalak, S., Golden, T., Clayton, M. (2011). A guide to forensic accounting investigation. USA: John Wiley Sons.

Systems of Equations on ACT Math Algebra Strategies and Practice Problems

Systems of Equations on ACT Math Algebra Strategies and Practice Problems SAT / ACT Prep Online Guides and Tips If you’ve already tackled your single variable equations, then get ready for systems of equations. Multiple variables! Multiple equations! (Whoo!) Even better, systems of equations questions will always have multiple methods with which to solve them, depending on how you like to work best. So let us look not only at how systems of equations work, but all the various options you have available to solve them. This will be your complete guide to systems of equations questions- what they are, the many different ways for solving them, and how you’ll see them on the ACT. Before You Continue You will never see more than one systems of equations question per test, if indeed you see one at all. Remember that quantity of questions answered (as accurately as possible) is the most important aspect of scoring well on the ACT, because each question is worth the same amount of points. This means that you should prioritize understanding the more fundamental math topics on the ACT, like integers, triangles, and slopes. If you can answer two or three integer questions with the same effort as you can one question on systems of equations, it will be a better use of your time and energy. With that in mind, the same principles underlying how systems of equations work are the same for other algebra questions on the test, so it is still a good use of your time to understand how they work. Let's go tackle some systems questions, then! Whoo! What Are Systems of Equations? Systems of equations are a set of two (or more) equations that have two (or more) variables. The equations relate to one another, and each can be solved only with the information that the other provides. Most of the time, a systems of equations question on the ACT will involve two equations and two variables. It is by no means unheard of to have three or more equations and variables, but systems of equations are rare enough already and ones with more than two equations are even rarer than that. It is possible to solve systems of equations questions in a multitude of ways. As always with the ACT, how you chose to solve your problems mostly depends on how you like to work best as well as the time you have available to dedicate to the problem. The three methods to solve a system of equations problem are: #1: Graphing #2: Substitution #3: Subtraction Let us look at each method and see them in action by using the same system of equations as an example. For the sake of our example, let us say that our given system of equations is: $$3x + 2y = 44$$ $$6x - 6y = 18$$ Solving Method 1: Graphing In order to graph our equations, we must first put each equation into slope-intercept form. If you are familiar with your lines and slopes, you know that the slope-intercept form of a line looks like: $y = mx + b$ If a system of equations has one solution (and we will talk about systems that do not later in the guide), that one solution will be the intersection of the two lines. So let us put our two equations into slope-intercept form. $3x + 2y = 44$ $2y = -3x + 44$ $y = {-3/2}x + 22$ And $6x - 6y = 18$ $-6y = -6x + 18$ $y = x - 3$ Now let us graph each equation in order to find their point of intersection. Once we graphed our equation, we can see that the intersection is at (10, 7). So our final results are $x = 10$ and $y = 7$ Solving Method 2: Substitution Substitution is the second method for solving a system of equations question. In order to solve this way, we must isolate one variable in one of the equations and then use that found variable for the second equation in order to solve for the remaining variable. This may sound tricky, so let's look at it in action. For example, we have our same two equations from earlier, $$3x + 2y = 44$$ $$6x - 6y = 18$$ So let us select just one of the equations and then isolate one of the variables. In this case, let us chose the second equation and isolate our $y$ value. (Why that one? Why not!) $6x - 6y = 18$ $-6y = -6x + 18$ $y = x - 3$ Next, we must plug that found variable into the second equation. (In this case, because we used the second equation to isolate our $y$, we need to plug in that $y$ value into the first equation.) $3x + 2y = 44$ $3x + 2(x - 3) = 44$ $3x + 2x - 6 = 44$ $5x = 50$ $x = 10$ And finally, you can find the numerical value for your first variable ($y$) by plugging in the numerical value you found for your second variable ($x$) into either the first or the second equation. $3x + 2y = 44$ $3(10) + 2y = 44$ $30 + 2y = 44$ $2y = 14$ $y = 7$ Or $6x - 6y = 18$ $6(10) - 6y = 18$ $60 - 6y = 18$ $-6y = -42$ $y = 7$ Either way, you have found the value of both your $x$ and $y$. Again, $x = 10$ and $y = 7$ Solving Method 3: Subtraction Subtraction is the last method for solving our systems of equations questions. In order to use this method, you must subtract out one of the variables completely so that you can find the value of the second variable. Do take note that you can only do this if the variables in question are exactly the same. If the variables are NOT the same, then we can first multiply one of the equations- the entire equation- by the necessary amount in order to make the two variables the same. In the case of our two equations, none of our variables are equal. $$3x + 2y = 44$$ $$6x - 6y = 18$$ We can, however, make two of them equal. In this case, let us decide to subtract our $x$ values and cancel them out. This means that we must first make our $x$’s equal by multiplying our first equation by 2, so that both $x$ values match. So: $3x + 2y = 44$ $6x - 6y = 18$ Becomes: $2(3x + 2y = 44)$ = $6x + 4y = 88$ (The entire first equation is multiplied by 2.) And $6x - 6y = 18$ (The second equation remains unchanged.) Now we can cancel out our $y$ values by subtracting the entire second equation from the first. $6x + 4y = 88$ - $6x - 6y = 18$ $4y - -6y = 70$ $10y = 70$ $y = 7$ Now that we have isolated our $y$ value, we can plug it into either of our two equations to find our $x$ value. $3x + 2y = 44$ $3x + 2(7) = 44$ $3x + 14 = 44$ $3x = 30$ $x = 10$ Or $6x - 6y = 18$ $6x - 6(7) = 18$ $6x - 42 = 18$ $6x = 60$ $x = 10$ Our final results are, once again, $x = 10$ and $y = 7$. If this is all unfamiliar to you, don't worry about feeling overwhelmed! It may seem like a lot right now, but, with practice, you'll find the solution method that fits you best. No matter which method we use to solve our problems, a system of equations will either have one solution, no solution, or infinite solutions. In order for a system of equations to have one solution, the two (or more) lines must intersect at one point so that each variable has one numerical value. In order for a system of equations to have infinite solutions, each system will be identical. This means that they are the same line. And, in order for a system of equations to have no solution, the $x$ values will be equal when the $y$ values are each set to 1. This means that, for each equation, both the $x$ and $y$ values will be equal. The reason this results in a system with no solution is that it gives us two parallel lines. The lines will have the same slope and never intersect, which means there will be no solution. For instance, For which value of $a$ will there be no solution for the systems of equations? $2y - 6x = 28$ $4y - ax = 28$ -12 -6 3 6 12 We can, as always use multiple methods to solve our problem. For instance, let us first try subtraction. We must get the two $y$ variables to match so that we can eliminate them from the equation. This will mean we can isolate our $x$ variables to find the value of our $a$. So let us multiply our first equation by 2 so that our $y$ variables will match. $2(2y - 6x = 28)$ = $4y - 12x = 56$ Now, let us subtract our equations $4y - 12x = 56$ - $4y - ax = 28$ $-12x - -ax = 28$ We know that our $-12x$ and our $-ax$ must be equal, since they must have the same slope (and therefore negate to 0), so let us equate them. $-12x = -ax$ $a = 12$ $a$ must equal 12 for there to be no solution to the problem. Our final answer is E, 12. If it is frustrating or confusing to you to try to decide which of the three solving methods â€Å"best† fits the particular problem, don’t worry about it! You will almost always be able to solve your systems of equations problems no matter which method you choose. For instance, for the problem above, we could simply put each equation into slope-intercept form. We know that a system of equations question will have no solution when the two lines are parallel, which means that their slopes will be equal. Begin with our givens, $2y - 6x = 28$ $4y - ax = 28$ And let’s take them individually, $2y - 6x = 28$ $2y = 6x + 28$ $y = 3x + 14$ And $4y - ax = 28$ $4y = ax + 28$ $y = {a/4}x + 7$ We know that the two slopes must be equal, so we will find $a$ by equating the two terms. $3 = a/4$ $12 = a$ Our final answer is E, 12. As you can see, there is never any â€Å"best† method to solve a system of equations question, only the solving method that appeals to you the most. Some paths might make more sense to you, some might seem confusing or cumbersome. Either way, you will be able to solve your systems questions no matter what route you choose. Typical Systems of Equations Questions There are essentially two different types of system of equations questions you’ll see on the test. Let us look at each type. Equation Question As with our previous examples, many systems of equations questions will be presented to you as actual equations. The question will almost always ask you to find the value of a variable for one of three types of solutions- the one solution to your system, for no solution, or for infinite solutions. (We will work through how to solve this question later in the guide.) Word Problems You may also see a systems of equations question presented as a word problem. Often (though not always), these types of problems on the ACT will involve money in some way. In order to solve this type of equation, you must first define and write out your system so that you can solve it. For instance, A movie ticket is 4 dollars for children and 9 dollars for adults. Last Saturday, there were 680 movie-goers and the theater collected a total of 5,235 dollars. How many movie-goers were children on Saturday? 88 112 177 368 503 First, we know that there were a total of 680 movie-goers, made up of some combination of adults and children. So: $a + c = 680$ Next, we know that adult tickets cost 9 dollars, children’s tickets cost 4 dollars, and that the total amount spent was 5,235 dollars. So: $9a + 4c = 5,235$ Now, we can, as always, use multiple methods to solve our equations, but let us use just one for demonstration. In this case, let us use substitution so that we can find the number of children who attended the theater. If we isolate our $a$ value in the first equation, we can use it in the second equation to solve for the total number of children. $a + c = 680$ $a = 680 - c$ So let us plug this value into our second equation. $9a + 4c = 5,235$ $9(680 - c) + 4c = 5235$ $6120 - 9c + 4c = 5235$ $-5c = -885$ $c = 177$ 177 children attended the theater that day. Our final answer is C, 177. You know what to look for and how to use your solution methods, so let's talk strategy. Strategies for Solving Systems of Equations Questions All systems of equations questions can be solved through the same methods that we outlined above, but there are additional strategies you can use to solve your questions in the fastest and easiest ways possible. 1) To begin, isolate or eliminate the opposite variable that you are required to find Because the goal of most ACT systems of equations questions is to find the value of just one of your variables, you do not have to waste your time finding ALL the variable values. The easiest way to solve for the one variable you want is to either eliminate your unwanted variable using subtraction, like so: Let us say that we have a systems problem in which we are asked to find the value of $y$. $$4x + 2y = 20$$ $$8x + y = 28$$ If we are using subtraction, let us eliminate the opposite value that we are looking to find (namely, $x$.) $4x + 2y = 20$ $8x + y = 28$ First, we need to set our $x$ values equal, which means we need to multiply the entire first equation by 2. This gives us: $8x + 4y = 40$ - $8x + y = 28$ - $3y = 12$ $y = 4$ Alternatively, we can isolate the opposite variable using substitution, like so: $4x + 2y = 20$ $8x + y = 28$ So that we don't waste our time finding the value of $x$ in addition to $y$, we must isolate our $x$ value first and then plug that value into the second equation. $4x + 2y = 20$ $4x = 20 - 2y$ $x = 5 - {1/2}y$ Now, let us plug this value for $x$ into our second equation. $8x + y = 28$ $8(5 - {1/2}y) + y = 28$ $40 - 4y + y = 28$ $-3y = -12$ $y = 4$ As you can see, no matter the technique you choose to use, we always start by isolating or eliminating the opposite variable we want to find. 2) Practice all three solving methods to see which one is most comfortable to you You’ll discover the solving method that suits you the best when it comes to systems of equations once you practice on multiple problems. Though it is best to know how to solve any systems question in multiple ways, it is completely okay to pick one solving method and stick with it each time. When you test yourself on systems questions, try to solve each one using more than one method in order to see which one is most comfortable for you personally. 3) Look extra carefully at any ACT question that involves dollars and cents Many systems of equations word problem questions are easy to confuse with other types of problems, like single variable equations or equations that require you to find alternate expressions. A good rule of thumb, however, is that it is highly likely that your ACT math problem is a system of equations question if you are asked to find the value of one of your variables and/or if the question involves money in some way. Again, not all money questions are systems of equations and not all systems of equation word problem questions involve money, but the two have a high correlation on the ACT. When you see a dollar sign or a mention of currency, keep your eyes sharp. Ready to tackle your systems problems? Test Your Knowledge Now let us test your system of equation knowledge on more ACT math questions. 1. The sum of real numbers $a$ and $b$ is 20 and their difference is 6. What is the value of $ab$? A. 51B. 64C. 75D. 84E. 91 2. For what value of $a$ would the following system of equations have an infinite number of solutions? $$2x-y=8$$ $$6x-3y=4a$$ A. 2B. 6C. 8D. 24E. 32 3. What is the value of $x$ in the following systems of equations? $$3x - 2y - 7 = 18$$ $$-x + y = -8$$ A. -1B. 3C. 8D. 9E. 18 Answers: E, B, D Answer Explanations: 1. We are given two equations involving the relationship between $a$ and $b$, so let us write them out. $a + b = 20$ $a - b = 6$ (Note: we do not actually know which is larger- $a$ or $b$. But also notice that it doesn't actually matter. Because we are being asked to find the product of $a$ and $b$, it does not matter if $a$ is the larger of the two numbers or if $b$ is the larger of the two numbers; $a * b$ will be the same either way.) Now, we can use whichever method we want to solve our systems question, but for the sake of space and time we will only choose one. In this case, let us use substitution to find the value of one of our variables. Let us begin by isolating $a$ in the first equation. $a + b = 20$ $a = 20 - b$ Now let's replace this $a$ value in the second equation. $a - b = 6$ $(20 - b) - b = 6$ $-2b = -14$ $b = 7$ Now we can replace the value of $b$ back into either equation in order to find the numerical value for $a$. Let us do so in the first equation. $a + b = 20$ $a + 7 = 20$ $a = 13$ We have found the numerical values for both our unknown variables, so let us finish with the final step and multiply them together. $a = 13$ and $b = 7$ $(13)(7)$ $91$ Our final answer is E, 91. 2. We know that a system has infinite solutions only when the entire system is equal. Right now, our coefficients (the numbers in front of the variables) for $x$ and $y$ are not equal, but we can make them equal by multiplying the first equation by 3. That way, we can transform this pairing: $2x - y = 8$ $6x - 3y = 4a$ Into: $6x - 3y = 24$ $6x - 3y = 4a$ Now that we have made our $x$ and $y$ values equal, we can set our variables equal to one another as well. $24 = 4a$ $a = 6$ In order to have a system that has infinite solutions, our $a$ value must be 6. Our final answer is B, 6. 3. Before we decide on our solving method, let us combine all of our similar terms. So, $3x - 2x - 7 = 18$ = $3x - 2y = 25$ Now, we can again use any solving method we want to, but let us choose just one to save ourselves some time. In this case, let us use subtraction. So we have: $3x - 2y = 25$ $-x + y = -8$ Because we are being asked to find the value of $x$, let us subtract out our $y$ values. This means we must multiply the second equation by 2. $2(-x + y = -8)$ $-2x + 2y = -16$ Now, we have a $-2y$ in our first equation and a $+2y$ in our second, which means that we will actually be adding our two equations instead of subtracting them. (Remember: we are trying to eliminate our $y$ variable completely, so it must become 0.) $3x - 2y = 25$ + $-2x + 2y = -16$ - $x = 9$ We have successfully found the value for $x$. Our final answer is D, 9. Good job! The tiny turtle is proud of you. The Take-Aways As you can see, there is a veritable cornucopia of ways to solve your systems of equations problems, which means that you have the ability to be flexible with them more than many other types of problems. So take heart that your choices are many for how to proceed, and practice to learn the method that suits you the best. What’s Next? Ready to take on more math topics? Of course you are! Luckily, we've got your back, with math guides on all the different math topics you'll see on the ACT. From circles to polygons, angles to trigonometry, we've got guides for your needs. Bitten by the procrastination bug? Learn why you're tempted to procrastinate and how to beat the urge. Want to skip to the most important math guides? If you only have time to tackle a few articles, take a look at two of the most important math strategies for improving your math score- plugging in answers and plugging in numbers. Knowing these strategies will help you take on some of the more challenging questions on the ACT in no time. Looking to get a perfect score? Check out our guide to getting a 36 on the ACT math section, written by a perfect-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. 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