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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 234 · 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 + 2y = 32 and 5x + y = 52 →
  2. 2.3x + y = 18 and 5x + y = 28 →
  3. 3.9x + 2y = −19 and 2x + 9y = −47 →
  4. 4.2x + y = 19 and x + 2y = 23 →
  5. 5.5x + 2y = −38 and 6x + y = −47 →
  6. 6.6x + 3y = −30 and 5x − 2y = −16 →
  7. 7.4x + 3y = 57 and 5x + 2y = 59 →
  8. 8.5x + 3y = 36 and 4x + 6y = 18 →
  9. 9.x + 8y = 56 and 8x + y = 70 →
  10. 10.9x + 7y = 25 and 7x + 9y = 23 →
  11. 11.3x − 6y = 57 and 4x + 6y = −36 →
  12. 12.2x + 6y = 38 and 6x + 2y = 34 →
  13. 13.2x − 3y = 2 and 5x + 5y = 55 →
  14. 14.3x + 2y = −18 and x − 3y = 16 →
  15. 15.x + 3y = 28 and 5x − 4y = −31 →
  16. 16.3x + 6y = −18 and 2x − 5y = −21 →
  17. 17.2x − y = 24 and 2x − 6y = 64 →
  18. 18.7x + 2y = 66 and 2x + 7y = 51 →
  19. 19.5x + 2y = −17 and 2x + 5y = 10 →
  20. 20.x − 2y = −7 and 6x + y = 49 →
  21. 21.5x − 2y = 59 and 4x + 2y = 22 →
  22. 22.x + 3y = −25 and 6x + 3y = −15 →
  23. 23.5x − 2y = −11 and 3x + 3y = 27 →
  24. 24.5x + 6y = 72 and 6x + 5y = 71 →
  25. 25.x + 5y = 11 and 6x − 2y = 2 →
  26. 26.x + y = 10 and 5x − 5y = −10 →
  27. 27.2x − 2y = 24 and 3x − 4y = 40 →
  28. 28.6x + y = 2 and 2x + 3y = 22 →
  29. 29.5x − y = 32 and 3x − y = 20 →
  30. 30.2x + y = 12 and 4x − 3y = −6 →
  31. 31.4x + 2y = −14 and 2x − 3y = 13 →
  32. 32.6x − 6y = 78 and x + 2y = 1 →
  33. 33.9x + y = 67 and x + 9y = 43 →
  34. 34.5x + 7y = −14 and 7x + 5y = −34 →
  35. 35.6x + 5y = 40 and 4x − y = 18 →
  36. 36.5x − 6y = −45 and 4x − 2y = −22 →
  37. 37.4x + 2y = 8 and 5x + 5y = 0 →
  38. 38.2x + 5y = 13 and 2x + y = −7 →
  39. 39.3x + 5y = 31 and 2x + 2y = 18 →
  40. 40.5x + 3y = 14 and 3x + 5y = 18 →

Answer key

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

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