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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.

Washington State Learning Standards learning standard: M.8.R.EE.8 · solving pairs of simultaneous linear equations and recognizing systems with no solution or infinitely many

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)

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, 0) a solution of both y = −4x − 20 and y = 3x + 15?

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

  2. Question 2

    Two numbers add to 11. Their difference is 1. What are the numbers?

    • 6 and 5
    • 7 and 4
    • 5 and 6
    • 11 and 1

  3. Question 3

    Adult tickets cost $12 and child tickets $4. 10 tickets cost $104 in all. How many adult tickets were sold?

    • 8
    • 7
    • 2
    • 9

  4. Question 4

    Where do the lines y = x + 5 and y = 2x + 4 meet?

    • (2, 7)
    • (6, 1)
    • (−1, 6)
    • (1, 7)
    • (1, 6)

  5. Question 5

    How many solutions does this system have? y = x − 3 and y = x − 7

    • Infinitely many solutions
    • No solution
    • Exactly one solution

  6. Question 6

    How many solutions does this system have? y = −3x + 2 and y = −3x

    • No solution
    • Exactly one solution
    • Infinitely many solutions

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