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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 516 · 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. 1.2x + 5y = 39 and 5x + 2y = 45 →
  2. 2.7x + 4y = −16 and 4x + 7y = 5 →
  3. 3.2x + y = 5 and 2x − 5y = 59 →
  4. 4.8x + 4y = 100 and 4x + 8y = 92 →
  5. 5.2x + 9y = 33 and 9x + 2y = 33 →
  6. 6.5x + 2y = −6 and 2x + 5y = 6 →
  7. 7.x + 6y = 29 and 2x + 6y = 22 →
  8. 8.2x + 4y = −4 and 3x − 5y = 16 →
  9. 9.8x + 6y = 84 and 6x + 8y = 70 →
  10. 10.7x + 9y = 1 and 9x + 7y = 15 →
  11. 11.x + 6y = 56 and 5x − 2y = −8 →
  12. 12.2x + 6y = 26 and 6x + 6y = 30 →
  13. 13.5x + 3y = −26 and 6x + 3y = −33 →
  14. 14.5x − 2y = −46 and 4x + 4y = 8 →
  15. 15.x + 5y = 1 and 3x + 2y = −23 →
  16. 16.2x + 8y = −32 and 8x + 2y = 22 →
  17. 17.2x − y = 9 and 5x + 4y = 55 →
  18. 18.4x + 2y = 18 and 6x − 6y = 18 →
  19. 19.6x − 5y = 11 and 3x − 4y = 7 →
  20. 20.5x + 4y = 37 and 5x + 6y = 33 →
  21. 21.7x + 2y = −36 and 2x + 7y = 9 →
  22. 22.2x + 6y = 22 and 6x + 2y = −14 →
  23. 23.2x − 3y = 4 and 4x + 5y = 30 →
  24. 24.2x + 5y = 31 and 2x − y = −23 →
  25. 25.3x − 3y = 9 and 4x + 5y = 21 →
  26. 26.4x + 4y = 56 and 2x + 3y = 37 →
  27. 27.2x − 2y = 10 and 3x − 2y = 19 →
  28. 28.4x + y = −25 and x + 4y = −40 →
  29. 29.4x + 6y = −28 and 6x − 4y = −16 →
  30. 30.x − 6y = −53 and 3x + 2y = 1 →
  31. 31.7x + 6y = 37 and 6x + 7y = 41 →
  32. 32.4x + 4y = −36 and 2x − 2y = 2 →
  33. 33.4x + y = 13 and x + 2y = 12 →
  34. 34.x + 7y = 58 and 7x + y = 22 →
  35. 35.4x + 5y = 44 and 5x + 4y = 46 →
  36. 36.4x + 7y = −1 and 7x + 4y = −10 →
  37. 37.3x − 5y = 11 and 3x − 4y = 13 →
  38. 38.5x + 2y = 23 and 2x − 2y = −2 →
  39. 39.2x − 5y = 7 and 2x + 4y = 16 →
  40. 40.x + 3y = 9 and 3x + y = 11 →

Answer key

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

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