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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 284 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.4x + 5y = 6 and x + 4y = 7 →
  2. 2.7x + 2y = 62 and 2x + 7y = 37 →
  3. 3.3x − 5y = −59 and 4x − y = −39 →
  4. 4.6x + 3y = 36 and 5x − 6y = −4 →
  5. 5.x + 2y = 9 and 5x − y = 12 →
  6. 6.7x + 6y = 26 and 6x + 7y = 26 →
  7. 7.4x + 8y = 40 and 8x + 4y = −16 →
  8. 8.4x + 6y = −32 and 4x + 4y = −28 →
  9. 9.5x − y = 8 and 3x + y = 8 →
  10. 10.4x − 5y = −77 and x + 6y = 46 →
  11. 11.2x + 5y = 21 and 3x + 5y = 19 →
  12. 12.4x + 9y = 113 and 9x + 4y = 108 →
  13. 13.5x + y = 54 and 6x − 4y = 18 →
  14. 14.4x + 5y = −13 and 6x + 2y = 8 →
  15. 15.7x + 5y = −88 and 5x + 7y = −80 →
  16. 16.3x + 2y = 24 and x + y = 11 →
  17. 17.2x + y = −20 and 4x + 5y = −52 →
  18. 18.2x + 9y = 3 and 9x + 2y = 52 →
  19. 19.6x + 2y = 42 and 2x + y = 16 →
  20. 20.4x + 3y = −3 and 6x + y = 13 →
  21. 21.6x − 3y = 27 and 3x − y = 18 →
  22. 22.4x + 3y = 29 and x + 4y = 17 →
  23. 23.3x + 8y = 25 and 8x + 3y = 30 →
  24. 24.2x + 8y = 4 and 8x + 2y = −14 →
  25. 25.4x + 2y = 4 and 3x + y = 1 →
  26. 26.3x + 6y = −30 and 6x + 3y = 3 →
  27. 27.2x + 6y = 34 and 5x + y = 15 →
  28. 28.5x + 2y = −17 and 2x + 5y = −32 →
  29. 29.5x + 3y = 43 and 3x + 5y = 45 →
  30. 30.3x + 2y = −4 and 3x + 4y = −2 →
  31. 31.3x + 7y = −32 and 7x + 3y = −8 →
  32. 32.6x + 6y = −36 and 4x + 3y = −26 →
  33. 33.x + 2y = 16 and x − 4y = −14 →
  34. 34.5x − 5y = 0 and 5x + y = −30 →
  35. 35.x + 5y = −32 and 2x − 2y = 32 →
  36. 36.7x + 6y = −97 and 6x + 7y = −98 →
  37. 37.2x + 3y = 11 and x − 3y = −8 →
  38. 38.2x + 6y = 38 and 6x + 2y = 18 →
  39. 39.3x + y = 3 and 2x − 2y = 10 →
  40. 40.4x + 3y = −23 and 3x + 6y = −6 →

Answer key

  1. x = −1, y = 2
  2. x = 8, y = 3
  3. x = −8, y = 7
  4. x = 4, y = 4
  5. x = 3, y = 3
  6. x = 2, y = 2
  7. x = −6, y = 8
  8. x = −5, y = −2
  9. x = 2, y = 2
  10. x = −8, y = 9
  11. x = −2, y = 5
  12. x = 8, y = 9
  13. x = 9, y = 9
  14. x = 3, y = −5
  15. x = −9, y = −5
  16. x = 2, y = 9
  17. x = −8, y = −4
  18. x = 6, y = −1
  19. x = 5, y = 6
  20. x = 3, y = −5
  21. x = 9, y = 9
  22. x = 5, y = 3
  23. x = 3, y = 2
  24. x = −2, y = 1
  25. x = −1, y = 4
  26. x = 4, y = −7
  27. x = 2, y = 5
  28. x = −1, y = −6
  29. x = 5, y = 6
  30. x = −2, y = 1
  31. x = 1, y = −5
  32. x = −8, y = 2
  33. x = 6, y = 5
  34. x = −5, y = −5
  35. x = 8, y = −8
  36. x = −7, y = −8
  37. x = 1, y = 3
  38. x = 1, y = 6
  39. x = 2, y = −3
  40. x = −8, y = 3

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