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Systems of Equations (Graphing)

A system of equations is simply a collection of equations that share a relationship. Here, you’ll learn how to solve two equations with two unknowns—two variables. You’ll learn three methods to solve systems of equations: Graphing, the substitution method, and the elimination method. Let’s start with graphing.




Solve both equations for y. This means that you should have y by itself on one side of both expressions. It looks something like this: y = ax + b.
Your expressions are now linear functions. Draw both of them in the same coordinate system.
Find the point of intersection and write down the corresponding values from the x-axis and the y-axis.

Example 1

Solve the system of equations y 2x = 2 (1) 4y + 4x = 20 (2)

First you solve (1) with respect to y:

y = 2x + 2

Then you solve (2) with respect to y: 4y + 4x = 20 4y = 4x + 20|÷ 4 y = x + 5

You may now plot the lines y = 2x + 2 and y = x + 5:

Two linear graphs intersecting at (1,4)

The point of intersection gives you x = 1 and y = 4.

ANSWER: (x,y) = (1, 4)

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Systems of Equations (Substitution)