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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.

Minnesota K-12 Academic Standards benchmark: 9.3.7.1 · solving systems of linear equations 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 Minnesota

In the Minnesota K-12 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: Minnesota Department of Education (MDE)

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 $5 and smoothies for $15. It sold 13 drinks for $95. Which system fits (j juices, s smoothies)?

    • 5j + s = 13 and j + 15s = 95
    • j + s = 95 and 5j + 15s = 13
    • j − s = 13 and 5j − 15s = 95
    • j + s = 13 and 5j + 15s = 95

  2. Question 2

    Solve the system: −4x + 4y = 4 and −x − 3y = 9

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

  3. Question 3

    Adult tickets cost $10 and child tickets $4. 11 tickets cost $56 in all. How many adult tickets were sold?

    • 3
    • 2
    • 9
    • 1

  4. Question 4

    Two numbers add to 34. Their difference is 16. What are the numbers?

    • 26 and 8
    • 25 and 9
    • 34 and 16
    • 24 and 10

  5. Question 5

    A snack bar sells juice for $8 and smoothies for $15. It sold 10 drinks for $94. Which system fits (j juices, s smoothies)?

    • j − s = 10 and 8j − 15s = 94
    • j + s = 10 and 8j + 15s = 94
    • 8j + s = 10 and j + 15s = 94
    • j + s = 94 and 8j + 15s = 10

  6. Question 6

    Two numbers add to 29. Their difference is 23. What are the numbers?

    • 25 and 4
    • 27 and 2
    • 29 and 23
    • 26 and 3

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