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7.3: Solving Linear Systems by Elimination through Addition or Subtraction

Difficulty Level: At Grade Created by: CK-12
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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.


Terms introduced in this lesson:

method of elimination

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*}x or \begin{align*}y\end{align*}y cancel, use \begin{align*}0x\end{align*}0x or \begin{align*}0y\end{align*}0y 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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