In this section, systems of equations are solved algebraically by graphing. A graphing calculator is needed.

If the two linear equations are both equal to the same variable, you do not need to manipulate the equations. You can graph the equations on your graphing calculator as they are written and then find the solution.

This method only works if the two equations are equal to the same variable.

Example: Solve

m = 2n – 2
m = 4n – 4

Click on the blanks to reveal the answers.

• Put both equations into the Y= equation editor of the calculator: Y1 = 2x – 2
  Y2 = 4x – 4
• Check for where the graphs intersect:
  
  The lines appear to cross at approximately Interactive button. Assistance may be required. __________ (1, 0).
• Check for where the table lists the Interactive button. Assistance may be required. __________ same Y1 and Y2 value.
  
  

X	Y1	Y2
-2	-6	-12
-1	-4	-8
0	-2	-4
1	0	0
2	2	4

• The Y1 and Y2 values are the same at x = Interactive button. Assistance may be required. __________ 1 ; the solution for the system of equations is the point Interactive button. Assistance may be required. __________ (1, 0) .