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9th grade · Math · Unit 7 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.2(I); A.5(C) · writing and solving systems of two linear 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 7 of 16 in 9th grade Math, after Linear Inequalities and before Data & Scatter Plots.

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: Texas Education Agency (TEA)

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

    Two numbers add to 41. Their difference is 1. What are the numbers?

    • 22 and 19
    • 21 and 20
    • 41 and 1
    • 20 and 21

  2. Question 2

    Adult tickets cost $7 and child tickets $5. 6 tickets cost $38 in all. How many adult tickets were sold?

    • 4
    • 2
    • 5
    • 3

  3. Question 3

    Solve the system: 2x + 4y = 24 and −4x + 4y = −24

    • (8, −2)
    • (2, 8)
    • (8, 2)
    • (9, 1)

  4. Question 4

    A snack bar sells juice for $4 and smoothies for $12. It sold 14 drinks for $104. Which system fits (j juices, s smoothies)?

    • 4j + s = 14 and j + 12s = 104
    • j + s = 104 and 4j + 12s = 14
    • j + s = 14 and 4j + 12s = 104
    • j − s = 14 and 4j − 12s = 104

  5. Question 5

    Solve the system: −3x − 3y = 0 and 4x + 3y = 0

    • (0, 0)
    • (1, −1)

  6. Question 6

    A snack bar sells juice for $3 and smoothies for $12. It sold 12 drinks for $63. Which system fits (j juices, s smoothies)?

    • j + s = 12 and 3j + 12s = 63
    • j + s = 63 and 3j + 12s = 12
    • j − s = 12 and 3j − 12s = 63
    • 3j + s = 12 and j + 12s = 63

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