Teaching Notes 3.18: Solving Systems of Equations Using the
Addition-or-Subtraction Method
The addition-or-subtraction method is an efficient way to solve systems of equations, especially
when the coefficients of one of the variables are opposites or are the same. Students may make
careless errors when they use this method, especially when they use the subtraction method.- Explain that the addition-or-subtraction method is a way (the substitution method is yet
another) for solving systems of equations. - Emphasize that this method is most useful when the coefficients of one of the variables are
opposites or when the coefficients of one of the variables are the same. In such cases, stu-
dents may add or subtract the equations, eliminating one of the variables. They will then
have an equivalent equation with one variable that they can solve. - Review the information and examples on the worksheet with your students. Emphasize that
students must add or subtract every term, including the numbers. Depending on your stu-
dents’ abilities, you may find it necessary to review the steps for solving equations. - Encourage your students to check their answer in both of the original equations, not the
rewritten equations. (Note:The check is not included with the examples.)
EXTRA HELP:
If the variables are on both sides of the equations, rewrite the equations so that all of the variables
are on one side.ANSWER KEY:
(1)a=6;b= 0 (2)a=4;b= 6 (3)x=2;y= 2 (4)a=0;b=− 2 (5)a=−3;b=− 1
------------------------------------------------------------------------------------------
(Challenge)Yes. The second equation can be rewritten as− 5 x+ 8 y=8.Additioncanthenbeused
to eliminate they-terms. The solution isx=8andy=6.
------------------------------------------------------------------------------------------122 THE ALGEBRA TEACHER’S GUIDE