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.

   Luz draws two lines on a four-quadrant grid. At which point (x, y) do line A and line B cross?

   (-2, -1)

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.

   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?

   • no solution
   • exactly one solution
   • infinitely many solutions
7. 6.

   Ren looks at the system y = 3x - 1 and y = 3x + 4 before graphing it. How many solutions does the system have?

   • infinitely many solutions
   • no solution
   • exactly one solution
8. 7.

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

   • no solution
   • exactly one solution
   • infinitely many solutions
9. 8.

   Bo's bean plant is 6 cm tall and grows 3 cm a week. The sunflower is 14 cm tall and grows 1 cm a week. At which point (weeks, cm) are they the same height?

   (4, 18)
10. 9.

    A red kite is 12 m up and climbs 3 m a minute. Ari's blue kite is 30 m up and climbs 1 m a minute. At which point (minutes, m) are they level?

    (9, 39)
11. 10.

    Tala has read 50 pages of a mystery and 20 pages of a comic. Each day, Tala reads 10 more mystery pages and 16 comic pages. At which point (days, pages) do the totals match?

    (5, 100)