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 (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.

2. 1.

   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)

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.

   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 in neither equation.
   • No: it works only in the second equation.
   • No: it works only in the first equation.
   • Yes: it works in both equations.
8. 5.

   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 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.
9. 6.

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

    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
11. 8.

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

    • infinitely many solutions
    • exactly one solution
    • no solution

12. 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.

13. 9.

    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

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?

    • no solution
    • exactly one solution
    • infinitely many solutions