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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.

Arizona Academic Standards learning standard: A1.A-REI.C.5; A1.A-REI.C.6; A1.A-CED.A.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 Arizona

In the Arizona Academic 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: Arizona Department of Education

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

    Solve the system: x + 3y = 23 and 3x + 4y = 39

    • (5, 6)
    • (6, 5)
    • (5, −6)

  2. Question 2

    A snack bar sells juice for $7 and smoothies for $14. It sold 10 drinks for $105. Which system fits (j juices, s smoothies)?

    • j − s = 10 and 7j − 14s = 105
    • 7j + s = 10 and j + 14s = 105
    • j + s = 105 and 7j + 14s = 10
    • j + s = 10 and 7j + 14s = 105

  3. Question 3

    Two numbers add to 16. Their difference is 10. What are the numbers?

    • 12 and 4
    • 16 and 10
    • 14 and 2
    • 13 and 3

  4. Question 4

    Adult tickets cost $12 and child tickets $2. 15 tickets cost $120 in all. How many adult tickets were sold?

    • 6
    • 10
    • 8
    • 9

  5. Question 5

    Adult tickets cost $12 and child tickets $4. 8 tickets cost $56 in all. How many adult tickets were sold?

    • 2
    • 4
    • 3
    • 5

  6. Question 6

    A snack bar sells juice for $7 and smoothies for $10. It sold 20 drinks for $176. Which system fits (j juices, s smoothies)?

    • j − s = 20 and 7j − 10s = 176
    • j + s = 176 and 7j + 10s = 20
    • 7j + s = 20 and j + 10s = 176
    • j + s = 20 and 7j + 10s = 176

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