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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.

Alaska content standards learning standard: 8.EE.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 Alaska

In the Alaska content 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: Alaska Department of Education and Early Development

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

    Is (2, 0) a solution of both y = −x + 2 and y = 3x − 2?

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

  2. Question 2

    How many solutions does this system have? y = x − 4 and y = −2x − 4

    • No solution
    • Infinitely many solutions
    • Exactly one solution

  3. Question 3

    Where do the lines y = −4x − 13 and y = −x − 4 meet?

    • (−2, −5)
    • (3, −1)
    • (−3, −1)
    • (−3, 0)
    • (−1, −3)

  4. Question 4

    Adult tickets cost $10 and child tickets $3. 13 tickets cost $67 in all. How many adult tickets were sold?

    • 9
    • 4
    • 5
    • 3

  5. Question 5

    Two numbers add to 36. Their difference is 20. What are the numbers?

    • 36 and 20
    • 27 and 9
    • 28 and 8
    • 29 and 7

  6. Question 6

    Adult tickets cost $10 and child tickets $2. 8 tickets cost $40 in all. How many adult tickets were sold?

    • 2
    • 5
    • 4
    • 3

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