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8th grade · Math · Unit 13 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.9 · the values of x and y that satisfy two 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 13 of 15 in 8th grade Math, after Angle Detective and before Variables on Both Sides.

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: Texas Education Agency (TEA)

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

    Where do the lines y = 4x + 12 and y = −2x − 12 meet?

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

  2. Question 2

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

    • Infinitely many solutions
    • Exactly one solution
    • No solution

  3. Question 3

    Is (−4, −8) a solution of both y = −4x − 24 and y = −2x − 14?

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

  4. Question 4

    Two numbers add to 27. Their difference is 11. What are the numbers?

    • 19 and 8
    • 27 and 11
    • 20 and 7
    • 18 and 9

  5. Question 5

    Adult tickets cost $7 and child tickets $3. 17 tickets cost $87 in all. How many adult tickets were sold?

    • 9
    • 10
    • 8
    • 6

  6. Question 6

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

    • Infinitely many solutions
    • No solution
    • Exactly one solution

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