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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 350 · 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 + 6y = −14 and x − 4y = 13 →
  2. 2.3x + 4y = 56 and 4x + 3y = 56 →
  3. 3.4x − 2y = −42 and 4x + y = −33 →
  4. 4.6x − 4y = −56 and 5x − 3y = −45 →
  5. 5.5x − 6y = −8 and 5x + 5y = 25 →
  6. 6.3x + y = −22 and x + 3y = −2 →
  7. 7.2x + y = 0 and x + y = −3 →
  8. 8.5x + 4y = −9 and 5x − 2y = −63 →
  9. 9.x + 6y = 48 and x + 3y = 27 →
  10. 10.6x + 9y = 57 and 9x + 6y = 48 →
  11. 11.2x + 4y = −4 and 2x + y = −7 →
  12. 12.3x + 9y = −15 and 9x + 3y = −21 →
  13. 13.x + 2y = 14 and 6x + 4y = 44 →
  14. 14.3x + 2y = 12 and 5x + 6y = 28 →
  15. 15.x + 2y = −15 and x − 6y = 49 →
  16. 16.9x + 3y = −27 and 3x + 9y = 63 →
  17. 17.3x − 2y = 4 and 3x + 5y = 11 →
  18. 18.x + 3y = 11 and 3x + 3y = 27 →
  19. 19.5x + 9y = −16 and 9x + 5y = 16 →
  20. 20.x − y = −6 and 6x + 5y = 63 →
  21. 21.4x + 3y = 1 and 6x − 4y = 10 →
  22. 22.6x + 4y = 62 and 4x + 6y = 68 →
  23. 23.6x + 5y = 55 and 5x + 6y = 55 →
  24. 24.3x + 5y = 30 and 5x + 3y = 34 →
  25. 25.5x − 2y = 51 and 4x + 2y = 12 →
  26. 26.2x + 8y = 46 and 8x + 2y = 34 →
  27. 27.6x − 4y = 32 and 4x + 2y = −2 →
  28. 28.8x + 9y = 3 and 9x + 8y = −3 →
  29. 29.7x + 2y = 58 and 2x + 7y = 23 →
  30. 30.7x + 2y = 10 and 2x + 7y = −55 →
  31. 31.x + 2y = −17 and 2x + 3y = −25 →
  32. 32.5x + 5y = 45 and 4x − 5y = 27 →
  33. 33.6x + 6y = −24 and 4x + 6y = −6 →
  34. 34.3x + 4y = −1 and 4x + 3y = −13 →
  35. 35.2x + 3y = −3 and 2x − y = 9 →
  36. 36.5x + 5y = −10 and 2x + 5y = −1 →
  37. 37.x − y = 11 and 3x + 4y = 12 →
  38. 38.3x + 2y = 4 and 6x + 2y = 10 →
  39. 39.4x − 3y = 0 and 3x − y = 5 →
  40. 40.6x + 5y = 58 and 5x + 6y = 63 →

Answer key

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

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