Teaching Notes 3.20: Solving Systems of Equations Using
a Variety of Methods
Solving systems of equations involves selecting an appropriate method for solving the system and
obtaining a solution. Choosing the most efficient method can be challenging for many students.- Explain to your students that there are three methods they can use to solve systems of
equations: (1) substitution, (2) addition or subtraction, and (3) multiplication with addition
or subtraction. Depending on the system of equations, one method may be more efficient
than the others. (A summary of when to use each method is included on the student
worksheet.) - Emphasize that regardless of which method is used, students should always try to obtain an
equation with one variable. They will then solve this equation and substitute the value of the
variable in one of the original equations to find the value of the other variable. - Review the information on the worksheetwith your students. Note that some systems of
equations may be solved by more than one method. Remind your students to always check
their work by substituting both values in the original equations.
EXTRA HELP:
Selecting the most efficient method for solving a system of equations makes the overall work
easier.ANSWER KEY:
(1)x=3;y= 0 (2)x=6;y= 3 (3)x=3;y= 1 (4)x=4;y= 0 (5)x=2;y= 1
(6)x=−3;y=− 2 (7)x=3;y= 2 (8)x=3;y= 1 (9)x=2;y= 0 (10)x=45;y=− 3
(11)x=−100;y= 72 (12)x=8;y= 4
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(Challenge)This is a system of equations when the coefficient of one of the variables is 1 and the
coefficient of the same variable in the other equation is−1.
------------------------------------------------------------------------------------------126 THE ALGEBRA TEACHER’S GUIDE