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9th grade · Math · Unit 12 of 18

Solving Systems

Elimination and substitution

What your child practices

Solving systems of two linear equations by elimination and substitution, and writing a system from a word problem.

California Content Standards learning standard: A-REI.5; A-REI.6; A-CED.3 · solving systems of linear equations and representing constraints with equations

How we explain it

Children can open this short lesson before they practice.

  1. Line the equations up, x under x and y under y.
  2. Add or subtract them so one variable cancels.
  3. Solve, then substitute back to find the other variable.

Example: Solve x + y = 10 and x − y = 4. Add: 2x = 14, so x = 7. 7 + y = 10, so y = 3. Answer: (7, 3)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A snack bar sells juice for $7 and smoothies for $15. It sold 6 drinks for $58. Which system fits (j juices, s smoothies)?

    • j + s = 58 and 7j + 15s = 6
    • j + s = 6 and 7j + 15s = 58
    • 7j + s = 6 and j + 15s = 58
    • j − s = 6 and 7j − 15s = 58

  2. Question 2

    Two numbers add to 20. Their difference is 4. What are the numbers?

    • 13 and 7
    • 20 and 4
    • 12 and 8
    • 11 and 9

  3. Question 3

    Solve the system: −x + 2y = 3 and x + y = 9

    • (6, 3)
    • (5, 4)
    • (5, −4)
    • (4, 5)

  4. Question 4

    Adult tickets cost $7 and child tickets $4. 7 tickets cost $34 in all. How many adult tickets were sold?

    • 3
    • 5
    • 1
    • 2

  5. Question 5

    Solve the system: −2x − y = −11 and 3x + 2y = 17

    • (5, −1)
    • (5, 1)
    • (6, 0)
    • (1, 5)

  6. Question 6

    Two numbers add to 19. Their difference is 5. What are the numbers?

    • 11 and 8
    • 13 and 6
    • 12 and 7
    • 19 and 5

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