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8th grade · Math · Unit 9 of 11

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.

Minnesota K-12 Academic Standards benchmark: 8.3.6.9; 8.2.4.3 · solving systems of linear equations and the kinds of solutions they can have

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 Minnesota

In the Minnesota K-12 Academic Standards, this is unit 9 of 11 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: 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

    Adult tickets cost $10 and child tickets $5. 11 tickets cost $90 in all. How many adult tickets were sold?

    • 7
    • 6
    • 4
    • 8

  2. Question 2

    Two numbers add to 27. Their difference is 25. What are the numbers?

    • 27 and 0
    • 26 and 1
    • 25 and 2
    • 27 and 25

  3. Question 3

    Where do the lines y = 3x − 2 and y = −3x + 4 meet?

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

  4. Question 4

    How many solutions does this system have? y = −x + 4 and y = −x + 7

    • No solution
    • Exactly one solution
    • Infinitely many solutions

  5. Question 5

    Is (−3, 4) a solution of both y = 2x + 10 and y = x + 6?

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

  6. Question 6

    How many solutions does this system have? y = −3x − 6 and y = 4x − 6

    • No solution
    • Exactly one solution
    • Infinitely many solutions

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