MathMaster Blog

A system of equations is a set of 2 or more equations with the same variables.

A solution to a system of equations is a set of values that makes each equation in the system true.

Elimination

In this method, you add or subtract the equations to eliminate one of the variables. Follow these steps:

Step 1: Rewrite the equations so that you can add or subtract to eliminate a variable. The coefficients of one of the variables are to be the same number or opposite numbers.

Step 2: Add or subtract the equations to eliminate one of the variables.

Step 3: Solve the equation you get for the variable.

Step 4: Substitute the value you got for the first variable into either of the equations and solve for the second variable.

Example:

Solve using elimination.

6x + 4y = –8

–3x − 4y = –16

Solution:

Step 1: Make sure the equations have opposite x terms or opposite y terms

The y terms (4y and –4y) are already opposites.

Step 2: Add to eliminate the y terms, and then solve for x

6x + 4y = –8

+(-3x – 4y = –16)

3x + 0y = –24

Simplify

3x = – 24

Divide both sides by 3

x = – 8

Step 3: Input the result of Step 2 (x = – 8)into one of the original equations and solve it

6x + 4y = – 8

6( –8) + 4y = – 8

– 48 + 4y = – 8

4y = 40

y = 10

Answer: ( – 8, 10)