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

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Zee sketches two lines that cross left of the y-axis. At which point (x, y) do line A and line B cross?

   (-2, 2)

2. Read this first

   Use this

   Two tables (x | y), only three rows each. Table A: 0 | -7; 1 | -4; 2 | -1. Table B: 0 | 9; 1 | 8; 2 | 7.

3. 2.

   Noah makes two tables from two steady rules but stops after three rows to get a snack. If both tables keep going, which point (x, y) will be in both?

   (4, 5)
4. 3.

   Pia wants the point that works in both y = -2x + 5 and y = x + 8, with no guessing. At which point (x, y) do the two lines cross?

   (-1, 7)
5. 4.

   Jun graphs y = 2x + 3 and y = -x + 3 on the same grid. At which point (x, y) do the two lines cross?

   (0, 3)
6. 5.

   Milo tests the point (3, -1) on the system y = -x + 2 and y = 2x - 7. Is (3, -1) 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.
7. 6.

   Tala hopes (-1, -3) solves the system y = 4x + 1 and y = -2x - 4. Is (-1, -3) a solution of the system?

   • No: it works only in the first equation.
   • Yes: it works in both equations.
   • No: it works in neither equation.
   • No: it works only in the second equation.
8. 7.

   Ari checks the point (2, -4) for the system y = x - 5 and y = -3x + 2 twice, just to be sure. Is (2, -4) a solution of the system?

   • Yes: it works in both equations.
   • No: it works only in the first equation.
   • No: it works in neither equation.
   • No: it works only in the second equation.
9. 8.

   Noah graphs a system of two equations on a four-quadrant grid as line A and line B. How many solutions does the system have?

   • infinitely many solutions
   • no solution
   • exactly one solution
10. 9.

    Esme graphs two equations on a four-quadrant grid, and only one line shows up. How many solutions does the system have?

    • infinitely many solutions
    • no solution
    • exactly one solution
11. 10.

    Kira copies the system y = 2x + 5 and y = 5 + 2x from the board. How many solutions does the system have?

    • no solution
    • infinitely many solutions
    • exactly one solution