Method: Elimination Explanation: Equations are added to eliminate a variable.
Practice makes perfect
Consider that we add two equations in two variables in a system of linear equations and end up with an equation in one variable. Let's visualize this situation with an example of a system.
2x-y= 3 & (I) x+y= 6 & (II)
We will add these equations using the Addition Property of Equality.
2x-y+ x+y= 3+ 6
Let's simplify this equation by adding and subtracting terms.
3x=9
We ended up with an equation in the variable x and eliminated the variable y. Therefore, we can conclude that we used the Elimination Method to solve the system.
Extra
Steps of the Elimination Method
Let's review the steps that we need to follow when solving a system of equations by the Elimination Method.
What is done?
Step I
Gather all like terms on the same sides of the equations.
Step II
Check if the coefficients of one of the variables in both equations are additive inverses of each other or the exact same number. If not, multiply or divide the equations by a constant so that one of the variable terms has the same or opposite coefficients.
Step III
Add or subtract equations in the system. This will result in one equation in one variable.
Step IV
Solve the obtained equation in one variable.
Step V
Substitute the result into one of the equations to find the other variable.
