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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 30 · 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 + y = −25 and 6x + 5y = −13 →
  2. 2.6x − y = −40 and 2x + y = −8 →
  3. 3.3x + 5y = −16 and 5x + 3y = 16 →
  4. 4.8x + 2y = 34 and 2x + 8y = 16 →
  5. 5.2x + 2y = −26 and 2x − 2y = −10 →
  6. 6.x − 2y = −4 and 5x − 6y = −16 →
  7. 7.5x − y = 35 and 5x + 4y = 60 →
  8. 8.3x + 6y = 21 and x + y = 0 →
  9. 9.2x + 8y = −6 and 8x + 2y = −54 →
  10. 10.3x − 2y = 8 and 3x + 6y = 0 →
  11. 11.3x + 9y = 90 and 9x + 3y = 78 →
  12. 12.8x + 5y = 29 and 5x + 8y = 23 →
  13. 13.6x − 3y = 0 and 4x + y = 12 →
  14. 14.2x + 6y = −22 and 4x − 6y = −26 →
  15. 15.2x + 5y = −4 and 4x + 2y = 24 →
  16. 16.x + y = 0 and 2x + 5y = −6 →
  17. 17.x + 4y = 6 and 6x + 2y = 14 →
  18. 18.3x + 5y = −27 and 5x + 3y = 3 →
  19. 19.2x + 3y = 29 and 2x + y = 11 →
  20. 20.x + 8y = −46 and 8x + y = 10 →
  21. 21.8x + 6y = 86 and 6x + 8y = 96 →
  22. 22.5x + y = 20 and x + 5y = 28 →
  23. 23.x + 6y = −17 and 6x + y = −32 →
  24. 24.4x + 2y = −4 and 2x + 4y = 10 →
  25. 25.4x + 5y = −22 and 2x − 4y = −24 →
  26. 26.2x + 7y = 11 and 7x + 2y = 61 →
  27. 27.4x − 4y = 8 and x − 5y = 6 →
  28. 28.x + 5y = 23 and 2x + y = 1 →
  29. 29.3x + y = 25 and 3x + 5y = 29 →
  30. 30.3x + y = −7 and 6x − 6y = −30 →
  31. 31.5x + 4y = 35 and 4x + 5y = 37 →
  32. 32.5x + 7y = 51 and 7x + 5y = 33 →
  33. 33.9x + 3y = −60 and 3x + 9y = −36 →
  34. 34.4x + 4y = −16 and 4x + 3y = −9 →
  35. 35.5x − 5y = −60 and 6x + 3y = −36 →
  36. 36.6x − 3y = −39 and 6x + 2y = −4 →
  37. 37.6x + 5y = 72 and 3x + 5y = 51 →
  38. 38.x + 7y = 20 and 7x + y = −4 →
  39. 39.6x + 3y = −60 and 3x + 6y = −57 →
  40. 40.2x + 3y = 34 and 3x + 2y = 36 →

Answer key

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

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