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 | 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.

4. 2.

   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)

5. Use this

   Two tables (days | pages). Novel: 0 | 0; 1 | 15; 2 | 30; 3 | 45; 4 | 60; 5 | 75. Comic book: 0 | 24; 1 | 33; 2 | 42; 3 | 51; 4 | 60; 5 | 69.

6. 3.

   Zee is reading a novel and a comic book at the same time. The tables show the total pages read after each day. Which point (days, pages) is in both tables?

   (4, 60)
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 only in the second equation.
   • Yes: it works in both equations.
   • No: it works in neither equation.
10. 7.

    Jun checks the point (3, 9) for the system y = 2x + 2 and y = x + 6 before lunch. Is (3, 9) a solution of the system?

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

    Tala graphs a system of two equations as line A and line B. How many solutions does the system have?

    • infinitely many solutions
    • no solution
    • exactly one solution
12. 9.

    Milo graphs a system of two equations as line A and line B. How many solutions does the system have?

    • exactly one solution
    • no solution
    • infinitely many solutions

13. Use this

    Two tables (x | y). Table A: 0 | 3; 1 | 5; 2 | 7; 3 | 9; 4 | 11. Table B: 0 | 6; 1 | 8; 2 | 10; 3 | 12; 4 | 14.

14. 10.

    Noah makes a table for each equation in a system. Both tables follow steady rules. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution