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.

   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)
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
   • exactly one solution
   • infinitely many solutions
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.

   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)
5. 5.

   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)

6. 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.

7. 6.

   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)

8. 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.

9. 7.

   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)
10. 8.

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

    • exactly one solution
    • infinitely many solutions
    • no solution
11. 9.

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

    • no solution
    • infinitely many solutions
    • exactly one solution
12. 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?

    • exactly one solution
    • no solution
    • infinitely many solutions