# 7.3: Solving Linear Systems by Elimination through Addition or Subtraction

**At Grade**Created by: CK-12

## Learning Objectives

At the end of this lesson, students will be able to:

- Solve a linear system of equations using elimination by addition.
- Solve a linear system of equations using elimination by subtraction.
- Solve real-world problems using linear systems by elimination.

## Vocabulary

Terms introduced in this lesson:

- elimination
- method of elimination
- coefficient

## Teaching Strategies and Tips

Use Example 1 to motivate the elimination method.

- To find the cost of one banana, it makes sense to subtract the equations.
- In general, equations can be added or subtracted so that a variable cancels.

Show that in Example 2, equations can be added column-wise; each column representing a different variable. When \begin{align*}x\end{align*} or \begin{align*}y\end{align*} cancel, use \begin{align*}0x\end{align*} or \begin{align*}0y\end{align*} as placeholders.

In Example 3,

- Drawing a picture helps.
- Encourage students to label variables first. The two unknowns are the
*speed of the river*and the*speed of the canoe in still water*. - Compare going downstream to walking on a moving walkway in an airport terminal. Travelers walk faster than usual as their speeds are boosted by the walkway. The opposite is true going upstream and against the moving walkway.

## Error Troubleshooting

Remind students in *Review Problem* 3 to align the variables column-wise.

In *Review Problems* 4, 6, 7, and 9, encourage students to put the equation being subtracted in parentheses. This way, it will be easier to remember to distribute the negative.

General Tip: When subtracting two equations, remind students not to forget to subtract the constants on the right side.

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