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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 607 · 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 + 2y = 10 and 6x − 3y = 45 →
  2. 2.5x + 2y = 7 and 6x + 2y = 10 →
  3. 3.5x − 4y = −18 and 4x + 4y = 36 →
  4. 4.x − 3y = −8 and 2x + 5y = 6 →
  5. 5.6x + 3y = 72 and x + 6y = 45 →
  6. 6.5x + 2y = −27 and 2x + 5y = −15 →
  7. 7.7x + y = −33 and x + 7y = 9 →
  8. 8.4x + 3y = 15 and 3x + 4y = 13 →
  9. 9.3x + y = −23 and x + 3y = −5 →
  10. 10.7x + y = 62 and x + 7y = 2 →
  11. 11.x + 2y = −8 and 3x + 3y = 0 →
  12. 12.6x + 5y = −16 and 2x − 6y = 56 →
  13. 13.x − y = 3 and 2x + 4y = −48 →
  14. 14.6x + 3y = 51 and x − 2y = 6 →
  15. 15.2x + 8y = 6 and 8x + 2y = −66 →
  16. 16.5x + 5y = −40 and x + 2y = −9 →
  17. 17.x + 3y = −19 and x − y = 9 →
  18. 18.5x + 8y = 54 and 8x + 5y = 63 →
  19. 19.x − y = −12 and 6x + 5y = 5 →
  20. 20.6x − 4y = −52 and 6x + y = −32 →
  21. 21.2x − 4y = 52 and 4x + 2y = 14 →
  22. 22.8x + 5y = −3 and 5x + 8y = −36 →
  23. 23.7x + 2y = 2 and 2x + 7y = 52 →
  24. 24.3x + y = −11 and 6x + y = −26 →
  25. 25.x + 2y = 19 and 3x − 2y = 9 →
  26. 26.x + 3y = 12 and 5x + 2y = −31 →
  27. 27.2x − 6y = −42 and 4x + 6y = 78 →
  28. 28.4x + y = 20 and x + 4y = 20 →
  29. 29.x + 4y = −13 and 4x + y = 23 →
  30. 30.8x + 2y = 22 and 2x + 8y = 58 →
  31. 31.6x − 5y = −9 and 4x + y = 7 →
  32. 32.x + 6y = 19 and 6x − 3y = −42 →
  33. 33.4x − 2y = 30 and 4x − 3y = 29 →
  34. 34.5x + 6y = 57 and 6x + 5y = 64 →
  35. 35.6x + 6y = −66 and 4x + 2y = −32 →
  36. 36.x + 4y = −34 and 6x + 3y = −15 →
  37. 37.4x − 3y = −45 and 3x + y = −11 →
  38. 38.3x + y = 36 and 6x + 6y = 108 →
  39. 39.5x + 3y = 49 and 2x + 2y = 26 →
  40. 40.3x + 8y = 30 and 8x + 3y = −30 →

Answer key

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

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