# 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.

### 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.

Building On

### 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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