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

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Esme solves the system y = (1/2)x + 1 and y = (3/2)x - 5 with a table for each equation. At which point (x, y) do the two lines cross?

   (6, 4)
2. 2.

   Zee looks at the system y = (1/2)x + 3 and y = 0.5x - 2, one with a fraction and one with a decimal. How many solutions does the system have?

   • no solution
   • infinitely many solutions
   • exactly one solution
3. 3.

   Noah's bean plant is 5 cm and grows 4 cm a week. The pea plant grows 2 cm a week and was 17 cm after 2 weeks. Which point (weeks, cm) shows equal heights?

   (4, 21)
4. 4.

   Ren measures snow on two hills. Sunny hill: 36 cm, melting 5 cm a day. Shady hill: melting 2 cm a day, 20 cm after 2 days. Which point (days, cm) shows equal depths?

   (4, 16)
5. 5.

   Luz's bean plant is 12 cm tall and grows 2 cm a week. The pea plant was 16 cm after 2 weeks and also grows 2 cm a week. Are they ever the same height?

   • Never: they grow at the same speed.
   • Exactly once: the pea plant catches up.
   • Every week: they are always the same height.
6. 6.

   Tala graphs the heights of a rising kite and a kite coming down. The lines cross at (5, 30). What does that point mean?

   • After 5 minutes, the kites are 30 m apart.
   • At the start, both kites are 30 m high.
   • After 30 minutes, both kites are 5 m high.
   • After 5 minutes, both kites are 30 m high.
7. 7.

   Jun graphs the heights of a bean plant and a sunflower. The lines cross at (6, 15). What does that point mean?

   • After 6 weeks, both plants are 15 cm tall.
   • After 6 weeks, the plants are 15 cm apart.
   • After 15 weeks, both plants are 6 cm tall.
   • At the start, both plants are 15 cm tall.
8. 8.

   Esme graphs the temperature in a town that warms up and a town that cools down. The lines cross at (3, 6). What does that point mean?

   • At the start, both towns are at 6°F.
   • After 3 hours, both towns are at 6°F.
   • After 6 hours, both towns are at 3°F.
   • After 3 hours, the towns are 6°F apart.

9. Read this first

   Use this

   Two tables (x | y). Table A: 0 | -4; 1 | -2; 2 | 0; 3 | 2; 4 | 4; 5 | 6. Table B: 0 | 10; 1 | 8; 2 | 6; 3 | 4; 4 | 2; 5 | 0.

10. 9.

    Jun makes two tables, and the lines cross between two rows. At which point (x, y), written with decimals, do the lines cross?

    (3.5, 3)
11. 10.

    Milo solves the system 3x + y = 4 and 3x + y = -2 just by looking. How many solutions does the system have?

    • no solution
    • exactly one solution
    • infinitely many solutions