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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 741 · 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 + 8y = 8 and 8x + 4y = −20 →
  2. 2.7x + 9y = −15 and 9x + 7y = −1 →
  3. 3.6x + 4y = −34 and 4x + 6y = −6 →
  4. 4.3x − y = −18 and 5x + 4y = −13 →
  5. 5.4x + y = −35 and 2x + 5y = −13 →
  6. 6.3x + y = −19 and x + 3y = −9 →
  7. 7.x + 6y = 61 and x − 5y = −38 →
  8. 8.5x − 2y = 56 and 2x + 6y = −32 →
  9. 9.x + 2y = 23 and 4x + 2y = 44 →
  10. 10.2x + 9y = 68 and 9x + 2y = 75 →
  11. 11.x − 6y = 41 and 4x − 6y = 56 →
  12. 12.4x − y = −29 and x + 6y = −1 →
  13. 13.2x + 6y = 56 and 5x − 6y = −49 →
  14. 14.5x + 6y = −1 and 2x − y = −14 →
  15. 15.6x + 6y = 72 and 4x − y = 33 →
  16. 16.6x + 2y = −6 and 2x + 6y = −50 →
  17. 17.2x − 3y = −35 and 2x − y = −21 →
  18. 18.x + y = 12 and x + 5y = 44 →
  19. 19.5x − y = 37 and x − 3y = −1 →
  20. 20.4x + 9y = 32 and 9x + 4y = 7 →
  21. 21.8x + 4y = −4 and 4x + 8y = −56 →
  22. 22.7x + y = −13 and x + 7y = 53 →
  23. 23.5x + 3y = 48 and 3x + 5y = 32 →
  24. 24.5x + 8y = −17 and 8x + 5y = 4 →
  25. 25.3x + 3y = −9 and 6x + 4y = −10 →
  26. 26.2x + 2y = −2 and 6x − 2y = −46 →
  27. 27.3x + 5y = 29 and 5x + 3y = 43 →
  28. 28.2x + y = 9 and x + 2y = 6 →
  29. 29.5x + 9y = 41 and 9x + 5y = 29 →
  30. 30.5x + 5y = 25 and 5x + y = −3 →
  31. 31.9x + 8y = 99 and 8x + 9y = 105 →
  32. 32.2x + 7y = 27 and 7x + 2y = −18 →
  33. 33.3x − 6y = 6 and 5x − 4y = −2 →
  34. 34.6x − 2y = 14 and 4x − 3y = 6 →
  35. 35.8x + 6y = 82 and 6x + 8y = 72 →
  36. 36.2x − 3y = 27 and 3x − 4y = 39 →
  37. 37.3x + 4y = −15 and 4x + 3y = 1 →
  38. 38.4x + 5y = −7 and 4x + y = 21 →
  39. 39.4x + 3y = 15 and 3x + 4y = 27 →
  40. 40.5x − y = 13 and 3x − 4y = −16 →

Answer key

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

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