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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 270 · 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. 1.9x + y = −43 and x + 9y = 13 →
  2. 2.6x − 5y = −9 and 3x + 5y = 63 →
  3. 3.4x + 2y = 32 and 2x + 4y = 10 →
  4. 4.8x + 7y = −12 and 7x + 8y = −18 →
  5. 5.2x − 4y = 18 and 6x − 4y = 22 →
  6. 6.3x + 5y = 60 and 6x + y = 39 →
  7. 7.6x + y = 20 and 5x − 4y = −22 →
  8. 8.x + 6y = 10 and 5x − y = 19 →
  9. 9.4x + 5y = 72 and 5x + 4y = 72 →
  10. 10.8x + 6y = 86 and 6x + 8y = 82 →
  11. 11.9x + 4y = 89 and 4x + 9y = 54 →
  12. 12.3x − y = 15 and 3x + 4y = −30 →
  13. 13.4x − 4y = 4 and 6x + 6y = 66 →
  14. 14.3x + 9y = −78 and 9x + 3y = −18 →
  15. 15.x − 2y = −1 and 2x + 4y = 22 →
  16. 16.x + 5y = −38 and 5x + 5y = −30 →
  17. 17.5x − 6y = −9 and 4x + 2y = −48 →
  18. 18.9x + 7y = 89 and 7x + 9y = 87 →
  19. 19.5x + 5y = −5 and 3x + 6y = −15 →
  20. 20.6x + 4y = 72 and x − 6y = −48 →
  21. 21.2x + 8y = 44 and 8x + 2y = −4 →
  22. 22.4x + 2y = 18 and 2x + 4y = 0 →
  23. 23.3x − 3y = 21 and 4x + 6y = −22 →
  24. 24.2x + y = 4 and 2x + 5y = −20 →
  25. 25.2x − 5y = 11 and 2x − 2y = −4 →
  26. 26.6x + y = −51 and x − 2y = −15 →
  27. 27.2x + 3y = 5 and 3x + 2y = 5 →
  28. 28.6x + y = −4 and x + 6y = 11 →
  29. 29.4x + 5y = −51 and 5x + 4y = −48 →
  30. 30.3x + 6y = 33 and 5x − 3y = 3 →
  31. 31.3x − 6y = −18 and 2x − 3y = −6 →
  32. 32.4x + 5y = 2 and x + 3y = −3 →
  33. 33.5x + 6y = 4 and 3x + y = 18 →
  34. 34.4x + y = −33 and 6x + 6y = −36 →
  35. 35.4x + y = 6 and x + 4y = −6 →
  36. 36.7x + 3y = 25 and 3x + 7y = 45 →
  37. 37.x + 4y = 38 and 2x + 3y = 31 →
  38. 38.4x + 2y = 18 and 2x − y = 3 →
  39. 39.2x + 6y = 54 and 3x + y = 17 →
  40. 40.6x + y = −23 and 4x + 3y = −27 →

Answer key

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

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