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9th grade · Math · Unit 12 of 22

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.

New York State Learning Standards learning standard: AI-A.REI.6; AI-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 New York

In the New York State Learning Standards, this is unit 12 of 22 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: New York State Education Department (NYSED)

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 $3 and smoothies for $12. It sold 6 drinks for $36. Which system fits (j juices, s smoothies)?

    • 3j + s = 6 and j + 12s = 36
    • j − s = 6 and 3j − 12s = 36
    • j + s = 6 and 3j + 12s = 36
    • j + s = 36 and 3j + 12s = 6

  2. Question 2

    Adult tickets cost $9 and child tickets $5. 17 tickets cost $117 in all. How many adult tickets were sold?

    • 8
    • 7
    • 9
    • 6

  3. Question 3

    Two numbers add to 21. Their difference is 17. What are the numbers?

    • 21 and 17
    • 20 and 1
    • 18 and 3
    • 19 and 2

  4. Question 4

    Solve the system: 2x + 4y = −12 and −4x + 2y = −26

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

  5. Question 5

    A snack bar sells juice for $8 and smoothies for $10. It sold 21 drinks for $192. Which system fits (j juices, s smoothies)?

    • j + s = 21 and 8j + 10s = 192
    • 8j + s = 21 and j + 10s = 192
    • j + s = 192 and 8j + 10s = 21
    • j − s = 21 and 8j − 10s = 192

  6. Question 6

    Two numbers add to 46. Their difference is 8. What are the numbers?

    • 26 and 20
    • 28 and 18
    • 27 and 19
    • 46 and 8

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