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.

   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)
3. 3.

   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
4. 4.

   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?

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

   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?

   • At exactly one minute: the red kite catches up.
   • At every minute: they climb at the same speed.
   • Never: they stay 15 m apart.
6. 6.

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

7. 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.

8. 7.

   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)

9. 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. 8.

    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. 9.

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

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

    • infinitely many solutions
    • exactly one solution
    • no solution