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.

   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)
2. 2.

   Pia's red kite is 8 m up, climbing 5 m a minute. A green kite climbs 2 m a minute and was 29 m up after 3 minutes. Which point (minutes, m) shows them level?

   (5, 33)
3. 3.

   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)
4. 4.

   Kira watches two kites climb 3 m a minute each. The red kite starts 10 m up and the blue kite 25 m up. Will they ever be at the same height?

   • Never: they stay 15 m apart.
   • At every minute: they climb at the same speed.
   • At exactly one minute: the red kite catches up.
5. 5.

   Two kites at Zee's club start 6 m up. The red kite climbs 4 m a minute, the blue kite 2 m a minute. Are they ever at the same height?

   • Exactly once: at the start, minute 0.
   • Every minute: they start at the same height.
   • Never: one climbs faster than the other.
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?

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

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

8. Read this first

   Use this

   Two tables (x | y). Table A: 0 | 0; 1 | 3; 2 | 6; 3 | 9; 4 | 12. Table B: 0 | 6; 1 | 5; 2 | 4; 3 | 3; 4 | 2.

9. 8.

   Ren sees that no row is in both tables, though the lines do cross. At which point (x, y), written with decimals, do the lines cross?

   (1.5, 4.5)
10. 9.

    Pia looks at the system x + 2y = 7 and x + 2y = 10 without graphing it. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution
11. 10.

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

    • infinitely many solutions
    • no solution
    • exactly one solution