This equation system might be a case where I would apply the substitution method, although I generally prefer the elimination method. The second equation can be easily solved for u: $u=6-v$. Throughout many future lessons in this course for Linear Algebra.

We just subtract the first equation from the second equation in order to eliminate $y$.īut in another case I would use the substitution method due the structure of the equations: Gaussian elimination (or row reduction) is a method used for solving linear systems. Here it is easy to see that this system can be solved with the elimination method. So I first of all I look whether the linear equation system can be solved with this method easily or not. In my case, I do prefer the elimination method. The original problem is made to be solved with one method. Many people prefer one method to another method due the personal preferences. There are two aspects which makes the substitution method inferior to the elimination method, and vice versa. This is exactly what we have after the second step of elimination. This is exactly what we have after the first step of elimination. Substituting this into the second and third equations yields If we solve the first equation for $x$, substitute, solve the first of the resulting two equations for $y$, then the result is exactly the same. With elimination, we would proceed as follows:Īt this point, we see that the original system of equations can be rewritten as Now, we can use the Addition Property of Equality to rewrite the first equation in our system, 2x+5y=12.Note that the elimination method is equivalent to the substitution method, where the choice of the variable for which we solve is constrained.Įxample: Consider the $3 imes 3$ system Therefore if one side of this equation equals z, then the other equals z as well. We know these statements are true because 6x-5y=3.5. We could separate each part and rewrite them as follows:

To start, let’s think about the second equation in two parts. We’re going to use this property to solve systems of linear equations by elimination. Therefore, if we were to add these equations, the y terms will cancel each other out.īut is adding equations a legitimate means to solve a system of equations? Consider the Addition Property of Equality, which states: If a=b, then a+c=b+c. These two numbers are additive inverses, which means they have a sum of 0. Let’s take a closer look at the system below.įirst, notice that the coefficients for the y terms are 5 and -5. Solving Systems of Equations by Elimination Examples Next, let’s put these steps to work with some examples of the elimination method. Start practicing Algebra 1 on Albert now! So, with this system of equations, the better option would be to solve the system of equations by elimination. Fractions can complicate the process of substitution. It’s clear that if we try to solve one of these equations for either x or y, we will end up with fractions. So, when is it best to use the elimination method? We might use the elimination method to solve the system of equations if rewriting the equations to isolate a variable is more complicated. Thus, all things being equal, we would probably use substitution if our system of equations were: In general, substitution is the best choice when one equation has a variable isolated. Substitution and elimination are two ways to solve systems of linear equations algebraically. Solving Systems of Linear Equations by Elimination This post will explain the process for solving systems of equations by elimination. In mathematics, we use the elimination method for solving systems of equations to eliminate one variable and solve for the other. We eliminate items on a to-do list throughout the day to simplify our schedules. Trying on clothes at a store helps us eliminate options and decide what to purchase. Elimination is a method of simplification.

Elimination algebra