How to Solve Systems of Linear Equations by Graphing

By Nicole Harms
The right tools will help you solve systems of linear equations accurately.
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When your teacher hands you a system of linear equations, which is a set of two or more equations, that you need to solve, you have several solving options. One option that works well with simple equations is the graphing method. This is a good choice because it gives you a visual idea of how you came to your answer. In order to use this method, you will need to be very accurate when you do your graphs.

How to Solve Systems of Linear Equations

Put both equations into slope-intercept form (y = mx +b). If you are solving y = x + 1 and 8 - 2y = -4x, you need to rearrange the second equation so that it is in slope-intercept form. When you solve for y, you get y = 2x +4.

Graph both equations on the same Cartesian plane using a straightedge. In the equation y = x + 1, 1 is the y-intercept, so plot a point at (0,1). Then, from that point, apply the slope. In this equation the slope, which is the coefficient of x, is 1, or 1/1. So from your y-intercept, go up 1 and over to the positive side 1. Plot this point, which is (1,2). Connect the points to make the first line.

Graph the second equation (y = 2x + 4) in the same manner. Start at the y-intercept, which is (0,4). From there, apply the slope, which in this example is 2/1. Go up 2 and over toward the positive side 1, which puts you at (6,1). Connect the points to make the second line.

Extend the two lines until you see where they intersect. They should intersect at (-3, -2). This is your solution.

Check your solution by plugging the point into each equation, using -3 for x and -2 for y. Both equations should come out true. For the first equation, -2 = -3 + 1, which gives you -2 = -2, and this is true. For the second equation, -4 (-3) = 8 - 2 (-2). This gives you 12 = 12, which is true. The answer is correct.

About the Author

Nicole Harms has been writing professionally since 2006, specializing in real estate, finance and travel. When she's not writing, she enjoys traveling and has visited several countries, including Israel, Spain, France and Guam. Harms received a Bachelor of Science in Education from Maranatha Baptist Bible College.