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.

   Milo solves y = (1/2)x + 4 and y = -x + 10 with two tables, picking x values that keep y whole. At which point (x, y) do the lines cross?

   (4, 6)
2. 2.

   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)
3. 3.

   Bo solves the system y = -(3/2)x + 2 and y = (1/2)x - 6 without a calculator in sight. At which point (x, y) do the two lines cross?

   (4, -4)
4. 4.

   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?

   • infinitely many solutions
   • no solution
   • exactly one solution
5. 5.

   Jun looks at the system y = (3/4)x - 2 and y = 0.75x - 2, one with a fraction and one with a decimal. How many solutions does the system have?

   • exactly one solution
   • infinitely many solutions
   • no solution
6. 6.

   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)
7. 7.

   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.
8. 8.

   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 5 minutes, both kites are 30 m high.
   • After 5 minutes, the kites are 30 m apart.
   • After 30 minutes, both kites are 5 m high.
9. 9.

   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?

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

10. 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.

11. 10.

    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)