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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 132 · 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 + 4y = −18 and 4x + 2y = −6 →
  2. 2.2x − 6y = −40 and 3x + 2y = 17 →
  3. 3.5x + 6y = 32 and 3x − 2y = 8 →
  4. 4.4x − y = −18 and 5x + y = −18 →
  5. 5.4x + 2y = 6 and 2x + 4y = −6 →
  6. 6.4x − 6y = −20 and x + 6y = 25 →
  7. 7.2x + 3y = 30 and 5x − 2y = 18 →
  8. 8.4x + 4y = 28 and 3x − 4y = 14 →
  9. 9.4x − 2y = 10 and 3x − 4y = 0 →
  10. 10.9x + y = −59 and x + 9y = −51 →
  11. 11.2x + 2y = −4 and 2x − y = −13 →
  12. 12.3x + 2y = 39 and 4x + 6y = 72 →
  13. 13.3x − y = 9 and 3x + 3y = −15 →
  14. 14.3x + 9y = 30 and 9x + 3y = −30 →
  15. 15.3x + 6y = −3 and 6x + 3y = 3 →
  16. 16.4x + 8y = 0 and 8x + 4y = −24 →
  17. 17.4x + 2y = 30 and 2x + 4y = 24 →
  18. 18.9x + y = 34 and x + 9y = 66 →
  19. 19.4x + 9y = −61 and 9x + 4y = 9 →
  20. 20.5x + 6y = −37 and 4x + 5y = −30 →
  21. 21.6x + 4y = −26 and 3x + 6y = −21 →
  22. 22.2x + 8y = 68 and 8x + 2y = 62 →
  23. 23.5x + 9y = 102 and 9x + 5y = 94 →
  24. 24.3x − 4y = 14 and 4x + y = −32 →
  25. 25.4x + y = −5 and x + 4y = 10 →
  26. 26.5x + 5y = 40 and 5x − 6y = 51 →
  27. 27.9x + 7y = 79 and 7x + 9y = 65 →
  28. 28.5x + y = 15 and x + 5y = 27 →
  29. 29.8x + 9y = −137 and 9x + 8y = −135 →
  30. 30.5x + 2y = 38 and 5x − 3y = 18 →
  31. 31.2x + 3y = −9 and 2x + 6y = −30 →
  32. 32.6x − 4y = −42 and x + 5y = 44 →
  33. 33.3x + 7y = 59 and 7x + 3y = 31 →
  34. 34.4x + 5y = 68 and x + 6y = 55 →
  35. 35.6x + 5y = 31 and 5x + 2y = 15 →
  36. 36.5x + 6y = 5 and x − 4y = −25 →
  37. 37.7x + y = −47 and x + 7y = 7 →
  38. 38.3x + 6y = −15 and 4x + 4y = −8 →
  39. 39.5x + 6y = 34 and 3x + 3y = 21 →
  40. 40.3x − 4y = −27 and x − y = −7 →

Answer key

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

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