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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 679 · 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. 1.6x − 3y = 24 and 6x − 2y = 18 →
  2. 2.7x + 2y = −11 and 2x + 7y = −16 →
  3. 3.2x + y = −27 and 2x + 2y = −36 →
  4. 4.5x + 3y = 24 and 3x + 2y = 14 →
  5. 5.8x + 9y = 99 and 9x + 8y = 105 →
  6. 6.x − 5y = 11 and x − 2y = 5 →
  7. 7.3x + 3y = −15 and 4x + y = −17 →
  8. 8.4x − 2y = −46 and 2x + y = −13 →
  9. 9.3x + 6y = 15 and 6x + y = 52 →
  10. 10.5x − 3y = −26 and 5x − 5y = −30 →
  11. 11.3x + y = 25 and 4x + 4y = 44 →
  12. 12.4x + y = −6 and x + 4y = 6 →
  13. 13.x + 6y = 37 and 3x − 5y = −27 →
  14. 14.9x + 3y = −51 and 3x + 9y = −57 →
  15. 15.2x + 2y = 30 and 2x − 2y = −6 →
  16. 16.2x + 6y = 38 and 3x + 5y = 29 →
  17. 17.4x + y = 25 and 2x − y = 5 →
  18. 18.6x − 6y = −30 and 5x + 3y = 31 →
  19. 19.4x + y = 16 and 6x + y = 20 →
  20. 20.2x + y = −2 and x + 2y = 8 →
  21. 21.4x + 2y = 8 and 2x + 4y = −20 →
  22. 22.3x + 8y = 51 and 8x + 3y = 81 →
  23. 23.4x − 3y = −10 and 5x + 4y = 34 →
  24. 24.6x + 8y = 42 and 8x + 6y = 42 →
  25. 25.x + 2y = −5 and 2x + y = −7 →
  26. 26.2x − 2y = −14 and x − 5y = −43 →
  27. 27.9x + 2y = −36 and 2x + 9y = 69 →
  28. 28.2x + 2y = 6 and 3x − 3y = 21 →
  29. 29.x − 3y = −17 and 6x + 2y = 58 →
  30. 30.4x + 5y = 33 and x + 2y = 12 →
  31. 31.x + 3y = 29 and 3x + y = 31 →
  32. 32.4x + 6y = 64 and 6x + 4y = 66 →
  33. 33.2x + 2y = 20 and 4x + 2y = 34 →
  34. 34.2x + 3y = −11 and 6x + 3y = −39 →
  35. 35.2x − 3y = 25 and 6x + 3y = −9 →
  36. 36.6x − 2y = 2 and 5x + 6y = 40 →
  37. 37.3x + 6y = 21 and 3x + 5y = 17 →
  38. 38.6x − y = 46 and 2x + y = 18 →
  39. 39.6x + 3y = 30 and 3x + 6y = −21 →
  40. 40.6x + 3y = 45 and 5x + 2y = 33 →

Answer key

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

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