Solving Systems of Linear Equations by Graphing

When using the graphing method to solve a system of linear equations, we can imagine each equation as a path, and the solution is where the two paths intersect. ‘X’ marks the spot – try it out!

The graphing method can be broken down into two main parts: graphing each equation and finding the point where they intersect.

Consider the following system of equations:

If we graph the equations, we can see that they intersect at ($0$, $5$):

We can check our answer by plugging the solution back into the system and making sure it checks out for both equations! 👌🏾

We typically see systems of linear equations with one solution, but they can also have no solutions or infinite solutions depending on if and how the lines intersect.