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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 666 · 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. 1.5x − 4y = 25 and 6x − 2y = 44 →
  2. 2.7x + 9y = −62 and 9x + 7y = −66 →
  3. 3.2x + y = 7 and x + 2y = −7 →
  4. 4.x + 2y = 1 and x + y = −1 →
  5. 5.4x − y = −19 and x + 3y = 5 →
  6. 6.5x − 6y = −32 and 2x − y = −10 →
  7. 7.2x + 3y = 29 and 3x + 2y = 21 →
  8. 8.5x − 3y = 9 and 2x + y = −14 →
  9. 9.3x − 4y = −20 and 2x − 3y = −16 →
  10. 10.5x + 3y = 14 and 5x + 5y = 30 →
  11. 11.2x − 2y = −22 and 4x − y = −29 →
  12. 12.4x − 4y = −20 and x + y = 1 →
  13. 13.5x + 2y = 0 and 2x + 3y = 11 →
  14. 14.3x + 4y = 29 and 4x + 3y = 27 →
  15. 15.6x − 4y = −20 and 2x + 3y = 2 →
  16. 16.5x + 6y = 5 and 6x − 4y = −50 →
  17. 17.4x + y = −19 and x + 4y = 14 →
  18. 18.x + 3y = 16 and 3x − y = 18 →
  19. 19.3x + y = −16 and 3x + 3y = 0 →
  20. 20.5x + y = 13 and 3x + 3y = 27 →
  21. 21.x + 6y = 43 and 6x − 2y = −8 →
  22. 22.x + y = −11 and 6x − 5y = 0 →
  23. 23.5x + 8y = −19 and 8x + 5y = −7 →
  24. 24.6x + 8y = −6 and 8x + 6y = 20 →
  25. 25.3x + 3y = 3 and 2x + 4y = 6 →
  26. 26.2x + 5y = 30 and 4x + 2y = 28 →
  27. 27.6x + 3y = 39 and 3x + 6y = 15 →
  28. 28.x + 5y = 7 and 5x + 5y = 15 →
  29. 29.x + 3y = 22 and 3x + y = 10 →
  30. 30.2x + 4y = 26 and 4x + 2y = 22 →
  31. 31.x + 8y = 78 and 8x + y = 57 →
  32. 32.5x + 5y = 75 and 4x − y = 15 →
  33. 33.x + 3y = −22 and 3x + 6y = −51 →
  34. 34.7x + 2y = −5 and 2x + 7y = −40 →
  35. 35.4x + 6y = 16 and 2x + 6y = 14 →
  36. 36.2x − y = −5 and 4x − y = −3 →
  37. 37.5x − 2y = 6 and x + 6y = 14 →
  38. 38.6x + 3y = −33 and 6x − 5y = −25 →
  39. 39.3x + 5y = 2 and 5x + 3y = −2 →
  40. 40.6x + 6y = 54 and 3x + 4y = 35 →

Answer key

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

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