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8th grade · Math · Unit 14 of 19

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.

New York State Learning Standards learning standard: NY-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 New York

In the New York State Learning Standards, this is unit 14 of 19 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: New York State Education Department (NYSED)

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 (5, −1) a solution of both y = −x + 4 and y = −2x + 9?

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

  2. Question 2

    Two numbers add to 18. Their difference is 8. What are the numbers?

    • 13 and 5
    • 18 and 8
    • 12 and 6
    • 14 and 4

  3. Question 3

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

    • Infinitely many solutions
    • No solution
    • Exactly one solution

  4. Question 4

    Where do the lines y = −3x − 20 and y = −4x − 25 meet?

    • (5, −5)
    • (−4, −8)
    • (−5, −4)
    • (−5, −5)

  5. Question 5

    Adult tickets cost $8 and child tickets $3. 6 tickets cost $28 in all. How many adult tickets were sold?

    • 1
    • 3
    • 2
    • 4

  6. Question 6

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

    • Infinitely many solutions
    • Exactly one solution
    • No solution

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