Caddell Prep Access Menu

Solving a System of Equations Graphically

Learn how to solve a system of equations graphically by plotting points and finding the point(s) of intersection.
There are two ways to find the point where your lines intersect.
The graphical way to find the point of intersection is to graph the equations by first writing the slope and y – intercept of each line. ( the “m” value and the “b” value. )
The slope is another way of measuring rise over run, or the ratio of distances from each point on the line. Start plotting points from each line’s y – intercept, and then plot the point from there using the slope of the line.
When you do this for each line, you get a point of intersection where the coordinates of that point are identical on both lines.
Another way to find the point of intersection is by making a table for the x and y values, and finding the coordinates by plugging each x value into the line equation for both lines.
An example:
 y = x + 1
 y = 2x - 1

 x-value  y = x + 1  y-value  coordinates
1  y = (1) + 1 2 (1,2)
2  y = (2) + 1 3 (2,3)
3  y = (3) + 1 4 (3,4)
4  y = (4) + 1 5 (4,5)
5  y = (5) + 1 6 (5,6)
 x-value  y = 2x - 1  y-value  coordinates
1  y = 2(1) - 1 1 (1,1)
2  y = 2(2) - 1 3 (2,3)
3  y = 2(3) - 1 5 (3,5)
4  y = 2(4) - 1 7 (4,7)
5  y = 2(5) - 1 9 (5,9)

So now you find the two identical coordinates from the two tables, and that coordinate would be your point of intersection.

  • Want full access to all of our free math tutorials & practice problems?

    Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II
    Sign Up Now