How to Solve Systems of Equations

In this lesson you will learn how to solve systems of equations.



Systems of equations usually have 2 equations and two variables. You can solve a system of equations by using one of the following methods.

• Graphing Method
• Substitution Method
• Elimination Method

Let’s consider the same system of two equations and solve it by using each of the above methods.

Graphing Method

2x – y = - 9
x + y = 6

Systems of Equations The graph of the first equation is the red line, and the graph of the second equation is the blue line. The x-coordinate of the point of intersection between the two graphs is x = -1 and the y-coordinate is y = -7. Therefore the solution of our system is x= - 1, y = -7.

Substitution Method

This method consists in expressing one variable in terms of the other one. In the second equation, x + y = 6, we can isolate x by subtracting y from both sides of the equation.

We get x = 6 – y

Replace x with 6 - y in the first equation.

2(6 - y) – y = - 9

Apply the distributive property.

12 – 2y –y = - 9

Combine the like terms.

12 – 3y = - 9

-3y = - 21

Divide by - 3 on both sides.

y = 7

To find x, return to x = 6 – y and replace y with y.

x = 6 – 7 = - 1

Elimination Method

2x – y = - 9
x + y = 6

Add the two equations to eliminate y.

(2x + x) + (- y +y) = - 9 + 6

3x + 0 = -3

3x = - 3

x = - 1

To find y replace x with -1 in the second equation.

-1 + y = 6

y = -7

Return from the Systems of Equations page to Algebra Videos or to 8th Grade CRCT Math.