Solving Systems of Linear Equations Using Graphing

A system of linear equations is just a set of two or more linear equations.

In two variables (x and y), the graph of a system of two equations is a pair of lines in the plane.

There are three possibilities:

• The lines intersect at zero points. (The lines are parallel.)
• The lines intersect at exactly one point. (Most cases.)
• The lines intersect at infinitely many points. (The two equations represent the same line.)

How to Solve a System of Equations Using the Graphing Method

This method is useful when you just need a rough answer, or you're pretty sure the intersection happens at integer coordinates. Just graph the two lines, and see where they intersect!

The two equations are in slope-intercept form.

The first line has a slope of 0.5 and a y-intercept of 2.

The second line has a slope of −2 and a y-intercept of −3.

Graph the two lines as shown.

The solution is where the two lines intersect, the point (–2, 1). That is, x = −2 and y = 1.