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8th grade · Math · Unit 13 of 17

Systems of Equations

Where two lines meet

What your child practices

Solving pairs of linear equations, checking a solution, telling when a system has no solution or infinitely many, and simple word problems.

Arizona Academic Standards learning standard: 8.EE.C.8 · finding and interpreting solutions to pairs of linear equations

How we explain it

Children can open this short lesson before they practice.

  1. The solution is the point that works in both equations.
  2. Set the two expressions for y equal and solve for x, then find y.
  3. Same slope, different intercept: no solution. Same line: infinitely many.

Example: Where do y = 2x + 1 and y = x + 4 meet? 2x + 1 = x + 4, so x = 3. y = 3 + 4 = 7. Answer: (3, 7)

Systems of Equations in Arizona

In the Arizona Academic Standards, this is unit 13 of 17 in 8th grade Math, after Exponent Rules and before Functions.

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: Arizona 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

    How many solutions does this system have? y = −3x and y = −x

    • No solution
    • Exactly one solution
    • Infinitely many solutions

  2. Question 2

    Where do the lines y = 3x − 10 and y = x − 4 meet?

    • (−3, −1)
    • (3, 0)
    • (4, 2)
    • (3, −1)
    • (−1, 3)

  3. Question 3

    Is (3, −1) a solution of both y = −4x + 11 and y = −x + 5?

    • No, it only works in the first
    • No, it works in neither
    • Yes, it works in both

  4. Question 4

    Adult tickets cost $10 and child tickets $3. 14 tickets cost $84 in all. How many adult tickets were sold?

    • 5
    • 7
    • 8
    • 6

  5. Question 5

    Two numbers add to 59. Their difference is 1. What are the numbers?

    • 31 and 28
    • 29 and 30
    • 30 and 29
    • 59 and 1

  6. Question 6

    Two numbers add to 36. Their difference is 8. What are the numbers?

    • 22 and 14
    • 36 and 8
    • 23 and 13
    • 21 and 15

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