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. 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. 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 (x | y), only three rows each. Table A: 0 | -7; 1 | -4; 2 | -1. Table B: 0 | 9; 1 | 8; 2 | 7.

4. 3.

   Noah makes two tables from two steady rules but stops after three rows to get a snack. If both tables keep going, which point (x, y) will be in both?

   (4, 5)

5. 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.

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)
7. 5.

   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.
   • Yes: it works in both equations.
   • No: it works only in the second equation.
   • No: it works only in the first equation.
8. 6.

   Noah graphs a system of two equations on a four-quadrant grid as line A and line B. How many solutions does the system have?

   • exactly one solution
   • infinitely many solutions
   • no solution
9. 7.

   Esme graphs two equations on a four-quadrant grid, and only one line shows up. How many solutions does the system have?

   • no solution
   • exactly one solution
   • infinitely many solutions
10. 8.

    Zee graphs a system of two equations on a four-quadrant grid as line A and line B. How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution
11. 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)
12. 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)