How can a graph or a table of values help us 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 we are solving by graphing, there are a few things to remember:
We 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.
We can also solve by using a table of values. We 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 the Solution
After we think we have found the solution using either method, we can check our solution by substituting both variables, usually x and y, into the equations. If we get an answer that looks like 1=1 or -25=-25, then we have solved correctly. If we get an answer like 8≠10, we did something incorrect and should check our work.
Extra
Additional Information
The most common method for solving systems of equations is actually to do it algebraically. We will learn about this in future chapters.
