![]() Now, the coefficients of y-terms are opposites.Īlso, both sides of an equation are equal. The two pairs of like terms of this system are the x-terms: 3x, 5x and the y-terms: –2y, 2y. Let’s take the system of two equations below for instance: ![]() To eliminate a variable from a system that has a pair of like terms with opposite coefficients, we need to add the equations. Let’s look at each of these cases in detail with examples. Substitute this value in one of the equations. Subtract or add the equations to eliminate a variable. Multiply one equation or both the equations by a non-zero constant so you get at least one pair of like terms with the same or opposite coefficients. ![]() If there aren’t any common or opposite coefficients: Subtract the equations to eliminate a variable. If the coefficients of one of the pairs are common: Plug the value so obtained in one of the equations. If the coefficients of one of the pairs are opposites:Īdd the equations to eliminate one variable. Identify the two pairs of like terms from both the equations. Let’s get a clear picture of how and where these properties are applied by looking at the steps of solving a system of equations in two variables. The properties of equality state that when we add, subtract, multiply, or divide both sides of an equation with the same number, the statement remains the same. ![]() Solving Systems of Equations by Elimination - Process Explainedīefore we explore the process, we need to recall the properties of equality, which forms the basis for eliminating a variable. In this lesson, we’ll learn how to solve a system of equations in two variables by elimination, a method that works by eliminating a variable to find the value of the other. I hope that this video over the comparison of methods for solving systems was helpful for you.The verb “eliminate” means to remove something. ![]() Now, let’s look at three different systems, and use what we’ve just learned to think through which method is most useful for each system. You would use an augmented matrix when the substitution and elimination method are either impractical or impossible altogether. You should use the elimination method when the same variables in all of the equations share the same coefficient, or when they share the same but negative coefficient. You should use the substitution method when one of the variables in one of your equations has already been isolated (it has a coefficient of 1). In this video, I’m assuming that you already know how to perform each method, so I want to spend a lot of time explaining not how to do them but rather when to use each method.įirst, I will verbally tell you when to use each method, then I will write out three different examples, and we will decide together which method is most efficient for each system. There are three different ways that you could do this: the substitution method, elimination method, and using an augmented matrix. So, in order to solve that problem, you need to be able to find the value of all the variables in each equation. If you recall, a system of equations is when you have more than one equation with unknown variables in a given problem. Hey, guys! Welcome to this video over comparing different methods for solving a system of equations. ![]()
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