Systems: one, none or infinitely many solutions, and the quickest method

Grade 9 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Rule A starts at 5 and steps up 2 each row. Rule B starts at -3 and steps up 2 each row.

2. 1.

   Ari writes two rules on a sticky note: y = 2x + 5 and y = 2x - 3. How many solutions does the system have?

   • No solution (inconsistent)
   • One solution (independent)
   • Infinitely many solutions (dependent)

3. Use this

   Rule A starts at 7 and steps down 3 each row. Rule B starts at 2 and steps down 3 each row.

4. 2.

   Bo programs two paths for a robot: y = -3x + 7 and y = -3x + 2. How many solutions does the system have?

   • One solution (independent)
   • No solution (inconsistent)
   • Infinitely many solutions (dependent)

5. Use this

   Rule A starts at 1 and steps up 4 each row. Rule B starts at 1 and steps up 4 each row.

6. 3.

   Esme copies two rules from a worksheet: y = 4x + 1 and y = 1 + 4x. How many solutions does the system have?

   • No solution (inconsistent), because the two lines are parallel
   • One solution (independent)
   • Infinitely many solutions (dependent)

7. Use this

   Rule A starts at 6 and steps down 2 each row. Rule B starts at 6 and steps down 2 each row.

8. 4.

   Jun sketches two rules for a board game: y = -2x + 6 and y = 6 - 2x. How many solutions does the system have?

   • No solution (inconsistent), because the two lines look parallel
   • Infinitely many solutions (dependent)
   • One solution (independent)

9. Use this

   Rule A starts at 2 and steps up 1 each row. Rule B starts at -4 and steps up 3 each row.

10. 5.

    Kira draws two rules on graph paper: y = x + 2 and y = 3x - 4. How many solutions does the system have?

    • No solution (inconsistent)
    • One solution (independent)
    • Infinitely many solutions (dependent)

11. Use this

    Rule A starts at 8 and steps down 2 each row. Rule B starts at -1 and steps up 1 each row.

12. 6.

    Luz tests two rules from a puzzle book: y = -2x + 8 and y = x - 1. How many solutions does the system have?

    • Infinitely many solutions (dependent)
    • One solution (independent)
    • No solution (inconsistent)

13. Table A (x | y)

    0 | 9; 1 | 7; 2 | 5; 3 | 3. Table B (x | y): 0 | 3; 1 | 1; 2 | -1; 3 | -3.

14. 7.

    Noah tracks two kites in a table. Both tables follow steady rules. How many solutions does the system have?

    • One solution (independent)
    • No solution (inconsistent)
    • Infinitely many solutions (dependent)

15. Table A (x | y)

    0 | 2; 1 | 7; 2 | 12; 3 | 17. Table B (x | y): 0 | 2; 1 | 7; 2 | 12; 3 | 17.

16. 8.

    Pia times two race turtles in a table. Both tables follow steady rules. How many solutions does the system have?

    • Infinitely many solutions (dependent)
    • One solution (independent)
    • No solution (inconsistent), since the two tables look different
17. 9.

    3x + 2y = 16. Equation 2: 5x - 2y = 8. Tala stacks 3x + 2y = 16 over 5x - 2y = 8. Which letter disappears when the two equations are added?

    • Neither letter disappears
    • Only y disappears
    • Only x disappears
18. 10.

    5x + 2y = 19. Equation 2: 5x + 3y = 24. Bo stacks 5x + 2y = 19 over 5x + 3y = 24. Which letter disappears when the two equations are added?

    • Only y disappears
    • Only x disappears
    • Neither letter disappears