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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 582 · 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 = −2 and 5x + 2y = 16 →
  2. 2.2x + 3y = −13 and x + y = −5 →
  3. 3.6x + y = 3 and 5x + y = 4 →
  4. 4.2x + 5y = 4 and 4x + 2y = −8 →
  5. 5.5x − 3y = −56 and 5x − 6y = −77 →
  6. 6.7x + 3y = 55 and 3x + 7y = 35 →
  7. 7.5x + 6y = 11 and x + 6y = −17 →
  8. 8.3x − 3y = 15 and x + 2y = −19 →
  9. 9.3x + 5y = 4 and 5x + 3y = 12 →
  10. 10.5x + y = 28 and 3x + 5y = 30 →
  11. 11.6x + 6y = 60 and 4x − 4y = −32 →
  12. 12.3x + 2y = 18 and x − 3y = −16 →
  13. 13.3x + 2y = 34 and 3x − 2y = 2 →
  14. 14.x + 5y = 1 and 2x − 3y = −11 →
  15. 15.4x + 2y = 8 and 2x + 4y = 22 →
  16. 16.2x + 4y = −6 and x − 6y = −19 →
  17. 17.9x + 3y = 54 and 3x + 9y = 42 →
  18. 18.2x + 6y = −46 and 6x − y = −5 →
  19. 19.x + 3y = 22 and 3x + y = 18 →
  20. 20.3x − 3y = −42 and 6x + 6y = −24 →
  21. 21.2x − 3y = −21 and 3x + 5y = 16 →
  22. 22.4x + 5y = 11 and 5x + 4y = 7 →
  23. 23.4x + 6y = −40 and 5x − 6y = 31 →
  24. 24.8x + 7y = 25 and 7x + 8y = 20 →
  25. 25.5x + 3y = 18 and 2x + y = 7 →
  26. 26.3x + 2y = 23 and 3x + 4y = 37 →
  27. 27.2x + 7y = −3 and 7x + 2y = 12 →
  28. 28.x + 2y = 7 and 5x + 4y = 11 →
  29. 29.6x + 5y = 28 and 4x + 3y = 20 →
  30. 30.3x + 6y = 42 and 6x + 3y = 39 →
  31. 31.3x + 4y = 25 and 4x + 2y = 10 →
  32. 32.4x − 5y = 1 and 5x + 3y = 29 →
  33. 33.5x − y = 17 and 4x − 5y = −20 →
  34. 34.3x + 4y = 16 and x − 4y = 0 →
  35. 35.9x + 8y = 70 and 8x + 9y = 66 →
  36. 36.5x − y = 8 and 2x − 6y = −36 →
  37. 37.4x + y = 21 and 4x − 2y = −6 →
  38. 38.6x + 2y = 10 and x − 5y = 23 →
  39. 39.3x + 2y = −3 and 5x + 5y = −20 →
  40. 40.6x + 2y = −20 and 4x + y = −16 →

Answer key

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

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