Illustrative Mathematics Grade 8, Unit 4, Lesson 13: Solving Systems of Equations

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Illustrative Math
Grade 8

Lesson 13: Solving Systems of Equations

Let’s solve systems of equations.

Illustrative Math Unit 8.4, Lesson 13 (printable worksheets)

Lesson 13 Summary

The following diagram show how to solve systems of equations using algebra.

Lesson 13.1 True or False: Two Lines

Use the lines to decide whether each statement is true or false. Be prepared to explain your reasoning using the lines.

1. A solution to 8 = -x + 10 is 2.
2. A solution to 2 = 2x + 4 is 8.
3. A solution to -x + 10 = 2x + 4 is 8.
4. A solution to -x + 10 = 2x + 4 is 2.
5. There are no values of x and y that make y = -x + 10 and y = 2x + 4 true at the same time.

• See Video for Whole Lesson

Lesson 13.2 Matching Graphs to Systems

Here are three systems of equations graphed on a coordinate plane:

1. Match each figure to one of the systems of equations shown here.
2. Find the solution to each system and then check that your solution is reasonable on the graph.

• Notice that the sliders set the values of the coefficient and the constant term in each equation.
• Change the sliders to the values of the coefficient and the constant term in the next pair of equations.
• Click on the spot where the lines intersect and a labeled point should appear. Open Applet

Lesson 13.3 Stacks of Cups

Your teacher will give you a page with 6 systems of equations.

1. Graph each system of equations by typing each pair of the equations in the applet, one at a time.
2. Describe what the graph of a system of equations looks like when it has . . .
   a. 1 solution
   b. 0 solutions
   c. infinitely many solutions
   Open Applet
   Use the applet to confirm your answer to question 2.

Are you ready for more?

The graphs of the equations Ax + By = 15 and Ax - By = 9 intersect at (2,1). Find A and B. Show or explain your reasoning.

• Show Answer

  Ax + By - 15 = Ax - By - 9
  2A + B - 15 = 2A - B - 9
  2B = 6
  B = 2

  2A + 3 = 15
  2A = 12
  A = 6

Lesson 13 Practice Problems

1. a. Write equations for the lines shown.
   b. Describe how to find the solution to the corresponding system by looking at the graph.
   c. Describe how to find the solution to the corresponding system by using the equations.
2. The solution to a system of equations is (5,-19). Choose two equations that might make up the system.
3. Solve the system of equations:
   y = 4x - 3
   y = -2x + 9
4. Solve the system of equations:
   y = 5/4 x - 2
   y = -1/4 x + 19
5. Here is an equation:
   a. Solve the equation by using the distributive property first.
   b. Solve the equation without using the distributive property.
   c. Check your solution.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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