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9th grade · Math · Unit 12 of 17

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.

Alaska 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)

Solving Systems in Alaska

In the Alaska content standards, this is unit 12 of 17 in 9th grade Math, after Linear Inequalities and before Linear or Exponential?.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alaska Department of Education and Early Development

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

    Two numbers add to 30. Their difference is 28. What are the numbers?

    • 28 and 2
    • 30 and 0
    • 29 and 1
    • 30 and 28

  2. Question 2

    A snack bar sells juice for $7 and smoothies for $15. It sold 16 drinks for $208. Which system fits (j juices, s smoothies)?

    • j − s = 16 and 7j − 15s = 208
    • j + s = 16 and 7j + 15s = 208
    • 7j + s = 16 and j + 15s = 208
    • j + s = 208 and 7j + 15s = 16

  3. Question 3

    Solve the system: −2x + 4y = −16 and x + 3y = −2

    • (−2, 4)
    • (4, −2)
    • (4, 2)
    • (5, −3)

  4. Question 4

    Adult tickets cost $9 and child tickets $2. 11 tickets cost $71 in all. How many adult tickets were sold?

    • 4
    • 7
    • 6
    • 8

  5. Question 5

    Solve the system: x + y = −1 and −2x − 4y = 6

    • (2, −3)
    • (1, −2)
    • (−2, 1)
    • (1, 2)

  6. Question 6

    A snack bar sells juice for $8 and smoothies for $15. It sold 14 drinks for $147. Which system fits (j juices, s smoothies)?

    • j − s = 14 and 8j − 15s = 147
    • 8j + s = 14 and j + 15s = 147
    • j + s = 147 and 8j + 15s = 14
    • j + s = 14 and 8j + 15s = 147

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