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How many solutions? Systems in standard form

Grade 8 math · 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 −6x + y = −2 and −18x + 3y = −6 have? Write one, none or infinite.
  2. How many solutions does the system 3x + y = 1 and 6x + 2y = 2 have? Write one, none or infinite.
  3. How many solutions does the system 6x + y = 9 and −3x + y = −1 have? Write one, none or infinite.
  4. How many solutions does the system 5x + y = 8 and 15x + 3y = 24 have? Write one, none or infinite.
  5. How many solutions does the system 5x + y = 7 and 5x + y = 5 have? Write one, none or infinite.
  6. How many solutions does the system −2x + y = 4 and −2x + y = 8 have? Write one, none or infinite.
  7. How many solutions does the system 8x + y = 9 and 8x + y = 10 have? Write one, none or infinite.
  8. How many solutions does the system 7x + y = 10 and 7x + y = 11 have? Write one, none or infinite.
  9. How many solutions does the system −5x + y = 5 and −10x + 2y = 10 have? Write one, none or infinite.
  10. How many solutions does the system 8x + y = 14 and 6x + y = 4 have? Write one, none or infinite.
  11. How many solutions does the system 6x + y = −4 and 6x + y = −1 have? Write one, none or infinite.
  12. How many solutions does the system −8x + y = −6 and −8x + y = −3 have? Write one, none or infinite.
  13. How many solutions does the system −x + y = 14 and −3x + 3y = 42 have? Write one, none or infinite.
  14. How many solutions does the system −3x + y = 12 and −3x + y = 15 have? Write one, none or infinite.
  15. How many solutions does the system 8x + y = 19 and −8x + y = −16 have? Write one, none or infinite.
  16. How many solutions does the system −11x + y = −9 and −11x + y = −8 have? Write one, none or infinite.
  17. How many solutions does the system −6x + y = 29 and −12x + 2y = 58 have? Write one, none or infinite.
  18. How many solutions does the system −14x + y = 19 and 10x + y = 16 have? Write one, none or infinite.
  19. How many solutions does the system 3x + y = 29 and 9x + 3y = 87 have? Write one, none or infinite.
  20. How many solutions does the system 9x + y = 3 and 9x + y = 5 have? Write one, none or infinite.
More free practice: fieldbooklearning.com/ca/practice/grade-8/how-many-solutions-systems-in-standard-form/

Answer key: How many solutions? Systems in standard form

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