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How many solutions does the system have?

Year 8 maths · Fieldbook Learning

Name ______________________ Date __________

Compare the slopes and intercepts. Different slopes give one solution. Same slope and same intercept give infinitely many. Same slope and different intercepts give none.

  1. How many solutions does the system y = −3x + 9 and y = −3x + 8 have? Write one, none or infinite.
  2. How many solutions does the system y = −3x + 4 and y = 3x have? Write one, none or infinite.
  3. How many solutions does the system y = 4x + 6 and y = 4x + 10 have? Write one, none or infinite.
  4. How many solutions does the system y = −4x − 2 and y = −4x − 2 have? Write one, none or infinite.
  5. How many solutions does the system y = 6x − 9 and y = 6x − 11 have? Write one, none or infinite.
  6. How many solutions does the system y = −4x + 6 and y = −4x + 2 have? Write one, none or infinite.
  7. How many solutions does the system y = −2x − 9 and y = −2x − 9 have? Write one, none or infinite.
  8. How many solutions does the system y = −x + 5 and y = −7x − 4 have? Write one, none or infinite.
  9. How many solutions does the system y = −10x + 11 and y = −10x + 14 have? Write one, none or infinite.
  10. How many solutions does the system y = −10x − 4 and y = −10x − 2 have? Write one, none or infinite.
  11. How many solutions does the system y = x − 7 and y = −5x + 13 have? Write one, none or infinite.
  12. How many solutions does the system y = 8x − 7 and y = −x − 7 have? Write one, none or infinite.
  13. How many solutions does the system y = 9x − 7 and y = 9x − 7 have? Write one, none or infinite.
  14. How many solutions does the system y = −4x − 2 and y = 4x − 10 have? Write one, none or infinite.
  15. How many solutions does the system y = 10x and y = 10x have? Write one, none or infinite.
  16. How many solutions does the system y = −2x − 19 and y = −2x − 21 have? Write one, none or infinite.
  17. How many solutions does the system y = −13x + 10 and y = −13x + 7 have? Write one, none or infinite.
  18. How many solutions does the system y = 8x + 4 and y = 8x + 4 have? Write one, none or infinite.
  19. How many solutions does the system y = 10x − 22 and y = −2x − 23 have? Write one, none or infinite.
  20. How many solutions does the system y = −12x − 30 and y = 8x + 29 have? Write one, none or infinite.
More free practice: fieldbooklearning.com/au/practice/year-8/how-many-solutions-does-the-system-have/

Answer key: How many solutions does the system have?

  1. none
  2. one
  3. none
  4. infinite
  5. none
  6. none
  7. infinite
  8. one
  9. none
  10. none
  11. one
  12. one
  13. infinite
  14. one
  15. infinite
  16. none
  17. none
  18. infinite
  19. one
  20. one