How can a graph or a table of values help you find a point that lies on two different lines?
See solution.
Practice makes perfect
One way to solve a system of equations is by graphing. When you are solving by graphing, there are a few things to remember:
You need to graph both equations on the same coordinate plane. This will make finding the point of intersection easier.
The point of intersection is the solution. However...
If the lines lie on top of one another, there are infinitely many solutions.
If the lines are parallel, there are no solutions.
You can also solve by using a table of values. You can substitute values into the equations and compare the results for each substitution. The input that gives the same output for both equations is the solution.
How to check your solution
After you think you have found the solution using either method, you can check your solution by substituting both variables, usually x and y, into the equations. If you get an answer that looks like 1=1 or -25=-25, then you solved correctly. You get an answer such as 8≠10, you did something incorrect and should check your work.
Extra
Additional Information
The most common method for solving systems of equations is actually to do it algebraically. You will learn about this in future chapters.
