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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 493 · 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.x + 2y = 14 and 3x − 2y = −22 →
  2. 2.6x + 2y = 34 and 6x − 6y = −30 →
  3. 3.x − 6y = −38 and x + 3y = 16 →
  4. 4.2x + 5y = −27 and 4x + 6y = −18 →
  5. 5.5x + 2y = 33 and 2x + y = 15 →
  6. 6.2x + 6y = −24 and 6x + 2y = −40 →
  7. 7.8x + 2y = −44 and 2x + 8y = −56 →
  8. 8.x + y = −6 and 4x + 2y = −14 →
  9. 9.4x + 6y = 66 and x + 3y = 30 →
  10. 10.9x + 5y = −27 and 5x + 9y = −71 →
  11. 11.x − 2y = −13 and 2x + y = −16 →
  12. 12.6x + 3y = 3 and 5x + 2y = 7 →
  13. 13.6x + 9y = 15 and 9x + 6y = 30 →
  14. 14.4x + 5y = 30 and 5x + 4y = 33 →
  15. 15.3x + 5y = 29 and 5x + 3y = 43 →
  16. 16.5x − 6y = −38 and 2x + y = 12 →
  17. 17.4x + 5y = 16 and 2x + 5y = 18 →
  18. 18.5x + 8y = 19 and 8x + 5y = −32 →
  19. 19.3x + 6y = 57 and x − 6y = −29 →
  20. 20.8x + 3y = 40 and 3x + 8y = 70 →
  21. 21.x + y = −7 and 2x + 3y = −20 →
  22. 22.2x + 4y = 34 and 3x − 2y = 11 →
  23. 23.3x − 5y = 0 and 2x + 5y = 25 →
  24. 24.4x + y = −32 and x + 6y = 15 →
  25. 25.5x + y = −31 and 5x + 5y = −15 →
  26. 26.9x + 6y = −63 and 6x + 9y = −72 →
  27. 27.x + 2y = −7 and 2x + y = −2 →
  28. 28.5x + 5y = −20 and 2x + 3y = −4 →
  29. 29.6x + 5y = −5 and 4x + 5y = 5 →
  30. 30.4x − y = −12 and 4x + 2y = −36 →
  31. 31.3x + 8y = 3 and 8x + 3y = 63 →
  32. 32.2x + 3y = 23 and 6x + 2y = 6 →
  33. 33.2x − y = 16 and 4x − 4y = 28 →
  34. 34.6x + 8y = −2 and 8x + 6y = −26 →
  35. 35.4x + 6y = 32 and x − y = −12 →
  36. 36.7x + 8y = −9 and 8x + 7y = −21 →
  37. 37.6x + 2y = −8 and 3x + 2y = −5 →
  38. 38.x + 2y = 3 and 6x + 2y = 38 →
  39. 39.2x + y = 11 and 3x − y = 24 →
  40. 40.6x − 5y = −33 and 5x − 6y = −33 →

Answer key

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

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