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9th grade · Math · Unit 17 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.

Alabama Course of Study content standard: AIP.10; AIP.13 · solving systems of linear equations and representing constraints in context

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 Alabama

In the Alabama Course of Study, this is unit 17 of 18 in 9th grade Math, after Function Notation and before Factoring & Quadratics.

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: Alabama State Department of Education (ALSDE)

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 $10. It sold 10 drinks for $88. Which system fits (j juices, s smoothies)?

    • 7j + s = 10 and j + 10s = 88
    • j − s = 10 and 7j − 10s = 88
    • j + s = 10 and 7j + 10s = 88
    • j + s = 88 and 7j + 10s = 10

  2. Question 2

    Adult tickets cost $11 and child tickets $2. 10 tickets cost $83 in all. How many adult tickets were sold?

    • 3
    • 7
    • 8
    • 6

  3. Question 3

    Two numbers add to 22. Their difference is 4. What are the numbers?

    • 12 and 10
    • 13 and 9
    • 14 and 8
    • 22 and 4

  4. Question 4

    Solve the system: x − 4y = −20 and −4x − 2y = −46

    • (8, 7)
    • (9, 6)
    • (7, 8)
    • (8, −7)

  5. Question 5

    Two numbers add to 14. Their difference is 8. What are the numbers?

    • 10 and 4
    • 14 and 8
    • 12 and 2
    • 11 and 3

  6. Question 6

    Solve the system: 4x − 4y = −16 and x − 4y = −25

    • (7, 3)
    • (4, 6)
    • (3, −7)
    • (3, 7)

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