Subscribe

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.

Maine Learning Results learning standard: HSA.REI.C.5; HSA.REI.C.6; HSA.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 Maine

In the Maine Learning Results, 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: Maine 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

    Adult tickets cost $8 and child tickets $5. 13 tickets cost $80 in all. How many adult tickets were sold?

    • 5
    • 4
    • 8
    • 6

  2. Question 2

    Solve the system: −4x − y = 9 and x − 2y = 9

    • (0, −6)
    • (−1, −5)
    • (−1, 5)
    • (−5, −1)

  3. Question 3

    Two numbers add to 11. Their difference is 3. What are the numbers?

    • 8 and 3
    • 11 and 3
    • 6 and 5
    • 7 and 4

  4. Question 4

    A snack bar sells juice for $6 and smoothies for $11. It sold 12 drinks for $87. Which system fits (j juices, s smoothies)?

    • j + s = 87 and 6j + 11s = 12
    • j + s = 12 and 6j + 11s = 87
    • j − s = 12 and 6j − 11s = 87
    • 6j + s = 12 and j + 11s = 87

  5. Question 5

    Adult tickets cost $11 and child tickets $2. 10 tickets cost $65 in all. How many adult tickets were sold?

    • 4
    • 6
    • 2
    • 5

  6. Question 6

    Two numbers add to 32. Their difference is 2. What are the numbers?

    • 32 and 2
    • 17 and 15
    • 18 and 14
    • 16 and 16

More 9th grade