Lesson 13
Solving Systems by Substitution
Lesson Narrative
In a previous lesson, students solved systems of linear equations by graphing. Here, they transition to solving systems algebraically—by substitution—and to reasoning about systems without a context.
The lesson activates and builds on what students have learned in grade 8 about solving by substitution. Students see that a system can be solved by replacing a variable with a number or with an expression, and that various substitutions can be done to solve the same system. They also begin to build an awareness of the kinds of systems that are conducive to being solved by substitution.
Students practice looking for and making use of structure as they identify the variables or expressions to substitute and ways to perform substitutions efficiently (MP7).
Learning Goals
Teacher Facing
 Recognize that a system can be efficiently solved by substitution if one variable is already isolated or can be easily isolated.
 Recognize that there are multiple ways to perform substitution to solve a system of equations.
 Solve systems of linear equations by substituting a variable with a number or an expression, and check solutions by substituting them back into the equations.
Student Facing
 Let’s use substitution to solve systems of linear equations.
Required Preparation
Access to graphing technology available for students.
Learning Targets
Student Facing
 I can solve systems of equations by substituting a variable or an expression.
 I know more than one way to perform substitution and can decide which way or what to substitute based on how the given equations are written.
CCSS Standards
Glossary Entries

solution to a system of equations
A coordinate pair that makes both equations in the system true.
On the graph shown of the equations in a system, the solution is the point where the graphs intersect.

substitution
Substitution is replacing a variable with an expression it is equal to.

system of equations
Two or more equations that represent the constraints in the same situation form a system of equations.
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