Teaching Notes 3.17: Solving Systems of Equations Using the
Substitution Method
Although several methods can be used to solve a system of equations, the substitution method is
among the most common. An error students often make is to substitute an incorrect expression
for a variable.- Explain that a system of equations is a set of two or more equations that have the same
variables. If there are two equations and two variables, the solution is an ordered pair of
numbers. - Explain that solving a system of equations is similar to solving one equation; there are no
new procedures. Students are essentially solving an equation and substituting the values.
Depending on the abilities of your students, you may find it helpful to review the steps for
solving equations. - Review the information and example on the worksheet with your students.
- Note that the second equation was used to solve forx. The second equation could have
been used to solve foryand also result in a correct solution. - Suggest to your students that, whenever possible, they solve an equation for a variable
whose coefficient is 1. This makes computation easier and is why the second equation in
the example was used to solve forx. - Emphasize that students must substitute the expression for a variable in the equation
that has not been used. In the example, because the second equation was used to solve
forx, the expression 5−ywas substituted forxin the first equation.
- Note that the second equation was used to solve forx. The second equation could have
EXTRA HELP:
The substitution method is easy to use when the coefficient of one of the variables is 1 or−1.ANSWER KEY:
(1)x=6;y= 3 (2)a=−4;b=− 2 (3)a=−8;b=− 16 (4)x=1;y=− 1 (5)x=29;y= 11
------------------------------------------------------------------------------------------
(Challenge)y−(10− 2 y)=5 was incorrectly written. It should bey− 10 + 2 y=5. The correct
solutions arey=5andx=0.
------------------------------------------------------------------------------------------120 THE ALGEBRA TEACHER’S GUIDE