Solve a system by graphing: one, none or infinitely many solutions

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Two tables (weeks | cm). Bean plant: 0 | 4; 1 | 7; 2 | 10; 3 | 13; 4 | 16. Sunflower: 0 | 10; 1 | 11; 2 | 12; 3 | 13; 4 | 14.

2. 1.

   Kira measures a bean plant and a sunflower every week (the sunflower is in no hurry). The tables show their heights. Which point (weeks, cm) is in both tables?

   (3, 13)

3. Use this

   Two tables (days | cm). Sunny hill: 0 | 20; 1 | 16; 2 | 12; 3 | 8; 4 | 4. Shady hill: 0 | 14; 1 | 12; 2 | 10; 3 | 8; 4 | 6.

4. 2.

   Tala checks the snow on two hills each day as it melts. The tables show the snow depth on each hill. Which point (days, cm) is in both tables?

   (3, 8)

5. Use this

   Two tables (days | buttons). Red jar: 0 | 2; 1 | 7; 2 | 12; 3 | 17; 4 | 22. Blue jar: 0 | 10; 1 | 11; 2 | 12; 3 | 13; 4 | 14.

6. 3.

   Esme adds buttons to two craft jars every day, one button at a time. The tables show how many buttons each jar holds. Which point (days, buttons) is in both tables?

   (2, 12)
7. 4.

   Noah sketches two lines on a grid with a freshly sharpened pencil. At which point (x, y) do line A and line B cross?

   (3, 4)
8. 5.

   Ren graphs two lines for a math club challenge. At which point (x, y) do line A and line B cross?

   (3, 8)
9. 6.

   Pia tests the point (2, 5) on the system y = 2x + 1 and y = x + 3. Is (2, 5) a solution of the system?

   • No: it works only in the first equation.
   • No: it works in neither equation.
   • Yes: it works in both equations.
   • No: it works only in the second equation.
10. 7.

    Luz thinks (2, 5) might solve the system y = 3x - 1 and y = x + 4. Is (2, 5) a solution of the system?

    • No: it works in neither equation.
    • No: it works only in the first equation.
    • Yes: it works in both equations.
    • No: it works only in the second equation.
11. 8.

    Kira graphs two equations and only one line shows up on the grid. How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution

12. Use this

    Two tables (x | y). Table A: 0 | 4; 1 | 7; 2 | 10; 3 | 13; 4 | 16. Table B: 2 | 10; 3 | 13; 4 | 16; 5 | 19; 6 | 22.

13. 9.

    Jun makes a table for each equation in a system, starting table B at a later row. Both follow steady rules. How many solutions does the system have?

    • infinitely many solutions
    • no solution
    • exactly one solution

14. Use this

    Two tables (x | y). Table A: 0 | 2; 1 | 3; 2 | 4; 3 | 5; 4 | 6. Table B: 0 | 2; 1 | 5; 2 | 8; 3 | 11; 4 | 14.

15. 10.

    Pia makes a table for each equation in a system (neat handwriting, too). Both tables follow steady rules. How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution