# Lesson 15

Solving Systems by Elimination (Part 2)

### Lesson Narrative

In this lesson, students continue to develop their understanding of solving systems by elimination. Students are given a system that represents the quantities and constraints in a situation. They interpret, in context, the solutions to the individual equations and to the system. They then use the context to make sense of the sum of the two equations and why it shares a solution with the equations in the given system. Along the way, students begin to formulate a logical explanation as to why adding (or subtracting) the two equations in a system can be helpful for identifying the solution to the system (MP3).

Students also practice solving systems by adding and subtracting equations and checking their solutions. They also encounter systems where one variable cannot be easily eliminated (given what they know at this point), motivating the need for another strategy.

### Learning Goals

Teacher Facing

• Explain (orally and in writing) why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.
• Practice solving systems of linear equations by adding or subtracting equations to eliminate a variable.
• Use a context to make sense of an equation that is the sum of two equations in a system, and to reason about why this equation shares a solution with the system.

### Student Facing

• Let’s think about why adding and subtracting equations works for solving systems of linear equations.

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)

### Student Facing

• I can explain why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.

Building Towards

### Glossary Entries

• elimination

A method of solving a system of two equations in two variables where you add or subtract a multiple of one equation to another in order to get an equation with only one of the variables (thus eliminating the other variable).

• 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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