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?

   • One solution (independent)
   • No solution (inconsistent)
   • 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?

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

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?

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

7. Use this

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

8. 4.

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

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

9. Table A (x | y)

   0 | 4; 1 | 7; 2 | 10; 3 | 13. Table B (x | y): 0 | 10; 1 | 13; 2 | 16; 3 | 19.

10. 5.

    Milo measures two plants in a table. Both tables follow steady rules. How many solutions does the system have?

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

11. Table A (x | y)

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

12. 6.

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

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

13. Table A (x | y)

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

14. 7.

    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

15. Table A (x | y)

    0 | 11; 1 | 7; 2 | 3; 3 | -1. Table B (x | y): 0 | 11; 1 | 7; 2 | 3; 3 | -1.

16. 8.

    Ren fills two buckets and logs a table. Both tables follow steady rules. How many solutions does the system have?

    • No solution (inconsistent)
    • One solution (independent)
    • Infinitely many solutions (dependent)
17. 9.

    4x + 3y = 17. Equation 2: 4x + y = 11. Zee stacks 4x + 3y = 17 over 4x + y = 11. Which letter disappears when the two equations are added?

    • Only y disappears
    • Only x disappears, because the x-numbers match
    • Neither letter disappears
18. 10.

    -3x + 2y = 1. Equation 2: 3x + 4y = 17. Ari stacks -3x + 2y = 1 over 3x + 4y = 17. Which letter disappears when the two equations are added?

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