Addition/Subtraction Method for Solving Systems of Two Equations

1. Algebraically manipulate both equations so that all the variables are on one side of the equal sign and in the same order. (Line the equations up, one on top of the other.)
2. If needed, multiply one of the equations by a constant so that there is one variable in each equation that has the same coefficient.
3. Subtract one equation from the other.
4. Solve the resulting equation for the one variable. (Use the technique described in previous units.)
5. Using the value found in the step 4, substitute it into either equation and solve for the remaining variable.
6. Substitute the values for both variables into the equation not used in step 5 to be sure our solution is correct.
   P = 2 + 2Q
   P = 10 – 6Q    P – 2Q = 2
   P + 6Q = 10           P = 2 + 2Q
   P = 2 + 2(1)
   P = 4    P = 10 – 6Q
   4 = 10 – 6(1)
   4 = 4.