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 | 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.

4. 2.

   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)
5. 3.

   Milo draws two straight lines on a grid for a puzzle, and the cat keeps sitting on it. At which point (x, y) do line A and line B cross?

   (2, 5)
6. 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)
7. 5.

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

   • Yes: it works in both equations.
   • No: it works only in the second equation.
   • No: it works in neither equation.
   • No: it works only in the first equation.
8. 6.

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

   • Yes: it works in both equations.
   • No: it works in neither equation.
   • No: it works only in the second equation.
   • No: it works only in the first equation.
9. 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?

   • Yes: it works in both equations.
   • No: it works in neither equation.
   • No: it works only in the first equation.
   • No: it works only in the second equation.
10. 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
11. 9.

    Kira graphs two equations and only one line shows up on the grid. 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. 10.

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

    • no solution
    • exactly one solution
    • infinitely many solutions