Worksheet

Solve a system by graphing: one, none or infinitely many solutions

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Luz draws two lines on a four-quadrant grid. At which point (x, y) do line A and line B cross?

  2. Esme graphs two lines for a puzzle page and draws a tiny star where they meet. At which point (x, y) do line A and line B cross?

  3. Zee sketches two lines that cross left of the y-axis. At which point (x, y) do line A and line B cross?

  4. Ren solves a system by making a table for each equation: y = 3x - 2 and y = x + 4. At which point (x, y) do the two lines cross?

  5. Milo tests the point (3, -1) on the system y = -x + 2 and y = 2x - 7. Is (3, -1) a solution of the system?

    • Yes: it works in both equations.
    • No: it works only in the first equation.
    • No: it works in neither equation.
    • No: it works only in the second equation.

  6. Ari checks the point (2, -4) for the system y = x - 5 and y = -3x + 2 twice, just to be sure. Is (2, -4) a solution of the system?

    • Yes: it works in both equations.
    • No: it works only in the second equation.
    • No: it works only in the first equation.
    • No: it works in neither equation.

  7. Kira copies the system y = 2x + 5 and y = 5 + 2x from the board. How many solutions does the system have?

    • no solution
    • infinitely many solutions
    • exactly one solution

  8. Luz looks at the system y = 4x - 3 and y = -x - 3 before graphing it. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution

  9. A red kite is 12 m up and climbs 3 m a minute. Ari's blue kite is 30 m up and climbs 1 m a minute. At which point (minutes, m) are they level?

  10. Tala has read 50 pages of a mystery and 20 pages of a comic. Each day, Tala reads 10 more mystery pages and 16 comic pages. At which point (days, pages) do the totals match?

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Solve a system by graphing: one, none or infinitely many solutions

Answer Key - Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.

  1. Luz draws two lines on a four-quadrant grid. At which point (x, y) do line A and line B cross?

    (-2, -1)

  2. Esme graphs two lines for a puzzle page and draws a tiny star where they meet. At which point (x, y) do line A and line B cross?

    (2, -3)

  3. Zee sketches two lines that cross left of the y-axis. At which point (x, y) do line A and line B cross?

    (-2, 2)

  4. Ren solves a system by making a table for each equation: y = 3x - 2 and y = x + 4. At which point (x, y) do the two lines cross?

    (3, 7)

  5. Milo tests the point (3, -1) on the system y = -x + 2 and y = 2x - 7. Is (3, -1) a solution of the system?

    • Yes: it works in both equations.
    • No: it works only in the first equation.
    • No: it works in neither equation.
    • No: it works only in the second equation.

  6. Ari checks the point (2, -4) for the system y = x - 5 and y = -3x + 2 twice, just to be sure. Is (2, -4) a solution of the system?

    • Yes: it works in both equations.
    • No: it works only in the second equation.
    • No: it works only in the first equation.
    • No: it works in neither equation.

  7. Kira copies the system y = 2x + 5 and y = 5 + 2x from the board. How many solutions does the system have?

    • no solution
    • infinitely many solutions
    • exactly one solution

  8. Luz looks at the system y = 4x - 3 and y = -x - 3 before graphing it. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution

  9. A red kite is 12 m up and climbs 3 m a minute. Ari's blue kite is 30 m up and climbs 1 m a minute. At which point (minutes, m) are they level?

    (9, 39)

  10. Tala has read 50 pages of a mystery and 20 pages of a comic. Each day, Tala reads 10 more mystery pages and 16 comic pages. At which point (days, pages) do the totals match?

    (5, 100)