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Two equations at once: 8th grade math

Systems of two linear equations. A free 8th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: systems of two linear equations.

Teach (10 min)

  • The solution of a system is the point where the two lines cross. It makes both equations true.
  • Read across to find x, then up or down to find y. Left of the y-axis and below the x-axis are negative.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/lineq.graph?lesson=8-lineq-graph-1&at=8

Exit ticket (5 min)

  • Use the first three questions on the printable sheet as a slip.

Printable sheet

Name: ____________________   Date: ____________

Two equations at once (8th grade)

  1. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  2. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  3. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  4. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  5. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  6. The two lines are the graphs of two equations, and they cross at one point.
    What is the y-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  7. The two lines are the graphs of two equations, and they cross at one point.
    What is the y-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  8. The two lines are the graphs of two equations, and they cross at one point.
    What is the y-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  9. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  10. The two lines are the graphs of two equations, and they cross at one point.
    What is the y-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  11. The two lines are the graphs of two equations, and they cross at one point.
    What is the x-coordinate of the solution?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
  12. The two lines cross at one point. Which ordered pair (x, y) is the solution of the system?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456Blue lineRed line
Key
  1. x = 4
  2. x = 3
  3. x = 3
  4. x = 1
  5. x = 2
  6. y = 3
  7. y = -2
  8. y = 4
  9. x = 1
  10. y = 2
  11. x = -1
  12. (1, −3)

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