# How to Solve an Algebra Problem by Elimination

By Tina Molly Lang

When you have two algebra equations, you might be asked to solve for variables "x" and "y." One way to solve an algebra problem is to use elimination. By using elimination you are in effect eliminating one variable to solve for another. This method is particularly effective when each variable has a coefficient in front of it, such as 5x, 4y or -2x. Here's how to solve an algebra problem using elimination.

Choose an example problem. 5x + 3y = 28 and 7x – 2y = 2.

Rewrite the equations so that the variables line up.5x + 3y = 287x – 2y = 2

Eliminate either the x or the y variable. In this case it is easier to eliminate the y variable. Multiply the top equation by 2 and the bottom equation by 3.2 (5x + 3y) = (28) 23 (7x – 2y) = (2) 3

The result is:10x + 6y = 5621x – 6y = 6

Add the two equations.10x + 6y = 5621x – 6y = 631x = 6231x / 31 = 62 / 31 x=2

To solve for y, substitute x=2 into the first equation.5x + 3y = 285(2) + 3y =2810 + 3y = 28

Solve for y by adding -10 to both sides and dividing by 3.10 + 3y = 28-10 = -10 3y = 18 3y / 3 = 18 / 3 y = 6

Check your answers by substituting x = 2 and y = 6 into both algebra equations. In each case, both sides should be equal.5x + 3y = 285(2) + 3(6) = 2810 + 18 = 2828 = 28

The first algebra equation checks out. Now check the second equation.7x – 2y = 27(2) – 2(6) = 214 – 12 = 22 = 2