How to solve systems of equations by Graphing

Step by step tutorial for systems of linear equations (in 2 variables)

Video on Solving by Graphing

The Graph Method

Example 1

What is the solution of the following system of equations?

$$ y = x + 1 \\ y = 2x $$

Step 1

Graph both equations

picture of systems of equations
Step 2

On the right, the graph of the two lines

The solution of the system is the point of intersection : (1,2)

picture of systems of equations

Practice Problems

Practice 1

Use the graph method to solve the system of equations below

$$ y = 2x +1 \\ y = 4x -1 $$

Step 1
Step 2
Step 1 is to Graph both equations

The solution of this system is the point of intersection : (1,3).

Practice 2

Solve the following system of linear equations by graphing.

$$ \text{ A) } 2y = 4x + 2 \\ \text{ B) }2y = -x + 7 $$

Step 1

Rewrite each equation in slope intercept form

$$ \text{ A) } 2y = 4x + 2 \\ \frac{1}{2} 2y = \frac{1}{2}(4x+2) \\ y = 2x +1 $$

$$ \text{ B) } 2y = 8x - 2 \\ \frac{1}{2} 2y = \frac{1}{2}( 8x - 2) \\ y = 4x +1 $$

This system of lines is the same system that we looked at in the last example.

Step 2

Graph each equation to find the point of intersection --which is the solution. (same as earlier problem)

back to Systems of Equations next to Solve By Elimination