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.

   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?

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

   Ari spots that the slopes in y = (2/3)x + 1 and y = (3/2)x + 1 use the same two digits. How many solutions does the system have?

   • exactly one solution
   • infinitely many solutions
   • no solution
4. 4.

   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)
5. 5.

   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)
6. 6.

   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?

   • Every week: they are always the same height.
   • Never: they grow at the same speed.
   • Exactly once: the pea plant catches up.
7. 7.

   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?

   • Every minute: they start at the same height.
   • Never: one climbs faster than the other.
   • Exactly once: at the start, minute 0.
8. 8.

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

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

9. Read this first

   Use this

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

10. 9.

    Kira is sure the two lines cross somewhere between the rows. At which point (x, y), written with decimals, do the lines cross?

    (2.5, 3.5)
11. 10.

    Noah looks closely at the system 2x + y = 5 and 4x + 2y = 10 before doing any work. How many solutions does the system have?

    • no solution
    • infinitely many solutions
    • exactly one solution