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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 72 · 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. 1.3x + 5y = 44 and 5x + 3y = 36 →
  2. 2.6x + 2y = 36 and 4x + 4y = 32 →
  3. 3.5x + 2y = 3 and 6x + y = 12 →
  4. 4.3x + 7y = 50 and 7x + 3y = 10 →
  5. 5.2x − 5y = 1 and 3x + 5y = 14 →
  6. 6.5x + 3y = 28 and 3x + 5y = 36 →
  7. 7.6x + 9y = −36 and 9x + 6y = −9 →
  8. 8.4x + y = 2 and 2x + y = 0 →
  9. 9.6x + 6y = 66 and 5x − 3y = 31 →
  10. 10.x + 8y = 51 and 8x + y = 30 →
  11. 11.2x + 4y = 20 and 4x + 2y = 28 →
  12. 12.4x − 4y = 56 and 5x + y = 34 →
  13. 13.5x + 4y = 53 and x + 3y = 15 →
  14. 14.8x + 3y = −73 and 3x + 8y = −48 →
  15. 15.9x + 8y = −20 and 8x + 9y = −31 →
  16. 16.6x + 4y = 44 and 4x + 6y = 56 →
  17. 17.4x + 2y = 18 and 2x + 4y = 12 →
  18. 18.7x + 8y = −98 and 8x + 7y = −97 →
  19. 19.3x + 5y = −16 and 3x + 3y = −6 →
  20. 20.7x + 2y = 36 and 2x + 7y = −9 →
  21. 21.5x + 9y = −36 and 9x + 5y = 36 →
  22. 22.6x + 2y = 24 and x − 6y = 61 →
  23. 23.8x + 3y = 16 and 3x + 8y = 61 →
  24. 24.4x − y = 14 and 2x − 5y = 16 →
  25. 25.2x + y = 6 and 4x + 5y = −6 →
  26. 26.x + 2y = 3 and x + y = 2 →
  27. 27.6x − 5y = 24 and 6x + y = 60 →
  28. 28.5x + y = 0 and 2x + y = −3 →
  29. 29.8x + 3y = 30 and 3x + 8y = 25 →
  30. 30.5x + 8y = 62 and 8x + 5y = 68 →
  31. 31.9x + 5y = −22 and 5x + 9y = −6 →
  32. 32.6x + 5y = 33 and 5x + 6y = 22 →
  33. 33.x + 4y = −4 and 4x + y = 29 →
  34. 34.x + 6y = −11 and 4x + 3y = −2 →
  35. 35.3x + 2y = 25 and 4x + y = 30 →
  36. 36.2x + 2y = −2 and 5x − y = 37 →
  37. 37.3x + 4y = 40 and 4x + 3y = 44 →
  38. 38.3x + 2y = −10 and 4x + 2y = −16 →
  39. 39.x + y = 3 and 5x + y = 23 →
  40. 40.3x + 3y = −12 and 5x + y = 12 →

Answer key

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

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