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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 541 · 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 + 6y = −3 and 5x + 6y = 15 →
  2. 2.3x + 4y = 42 and 6x + 6y = 66 →
  3. 3.4x + 3y = 15 and 5x + 5y = 20 →
  4. 4.4x + 2y = 10 and 5x − 5y = 50 →
  5. 5.3x + 4y = −2 and 3x + 3y = 0 →
  6. 6.3x + 6y = 15 and 6x + 3y = −33 →
  7. 7.4x + 5y = −18 and 3x + 5y = −11 →
  8. 8.6x − 6y = −72 and 2x + 2y = 0 →
  9. 9.6x + 6y = 0 and x − 3y = 36 →
  10. 10.6x + 2y = 2 and x − 5y = −37 →
  11. 11.8x + 9y = −45 and 9x + 8y = −57 →
  12. 12.6x + 4y = −38 and 5x + 3y = −30 →
  13. 13.2x − 5y = 39 and 4x − 5y = 53 →
  14. 14.6x − 5y = 17 and 5x − y = 30 →
  15. 15.9x + y = −73 and x + 9y = 63 →
  16. 16.2x + y = −3 and x + 2y = 6 →
  17. 17.6x − y = −57 and 4x + y = −33 →
  18. 18.5x + y = −9 and 6x − 3y = −15 →
  19. 19.x − y = −1 and 2x + 3y = 33 →
  20. 20.3x + 9y = 33 and 9x + 3y = 27 →
  21. 21.3x + 9y = 30 and 9x + 3y = 18 →
  22. 22.4x + y = 30 and x + 4y = 15 →
  23. 23.3x + 4y = −5 and 4x + 3y = −2 →
  24. 24.3x + 6y = 0 and 2x − 5y = −36 →
  25. 25.x − 3y = −7 and 5x + 6y = 28 →
  26. 26.5x + 2y = 26 and 2x + 5y = −19 →
  27. 27.x + y = 10 and 5x + 3y = 48 →
  28. 28.2x + y = −2 and 2x − 5y = −14 →
  29. 29.6x + 4y = 58 and 4x + 6y = 52 →
  30. 30.8x + 2y = 40 and 2x + 8y = 40 →
  31. 31.7x + 9y = −50 and 9x + 7y = −46 →
  32. 32.5x + y = 54 and 3x + y = 36 →
  33. 33.6x + 3y = −9 and 4x + y = 1 →
  34. 34.x + 2y = 9 and 2x + y = 6 →
  35. 35.3x + 5y = 11 and x − 4y = −2 →
  36. 36.3x + 2y = −10 and 6x − 6y = −90 →
  37. 37.6x + y = −19 and 6x − y = −29 →
  38. 38.3x − 2y = 19 and 3x − y = 20 →
  39. 39.5x + 5y = 10 and 4x − 3y = −48 →
  40. 40.2x + 2y = −16 and 2x + 6y = −24 →

Answer key

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

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