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

  3. Read this first

    Use this

    Two tables (hours | °F), only three rows each. Town A: 0 | -8; 1 | -4; 2 | 0. Town B: 0 | 4; 1 | 5; 2 | 6.

  4. On a cold morning, Luz records the temperature in two towns every hour. Both keep warming at a steady rate. At which point (hours, °F) are the towns equally warm?

  5. Pia wants the point that works in both y = -2x + 5 and y = x + 8, with no guessing. At which point (x, y) do the two lines cross?

  6. 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 second equation.
    • No: it works in neither equation.
    • No: it works only in the first equation.

  7. 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?

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

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

    • infinitely many solutions
    • exactly one solution
    • no solution

  9. Bo's bean plant is 6 cm tall and grows 3 cm a week. The sunflower is 14 cm tall and grows 1 cm a week. At which point (weeks, cm) are they the same height?

  10. 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?

  11. 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. 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)

  2. 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)

  3. Read this first

    Use this

    Two tables (hours | °F), only three rows each. Town A: 0 | -8; 1 | -4; 2 | 0. Town B: 0 | 4; 1 | 5; 2 | 6.

  4. On a cold morning, Luz records the temperature in two towns every hour. Both keep warming at a steady rate. At which point (hours, °F) are the towns equally warm?

    (4, 8)

  5. Pia wants the point that works in both y = -2x + 5 and y = x + 8, with no guessing. At which point (x, y) do the two lines cross?

    (-1, 7)

  6. 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 second equation.
    • No: it works in neither equation.
    • No: it works only in the first equation.

  7. 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?

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

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

    • infinitely many solutions
    • exactly one solution
    • no solution

  9. Bo's bean plant is 6 cm tall and grows 3 cm a week. The sunflower is 14 cm tall and grows 1 cm a week. At which point (weeks, cm) are they the same height?

    (4, 18)

  10. 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)

  11. 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)