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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 268 · 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. 1.4x + y = 14 and 3x + 3y = 15 →
  2. 2.6x + 8y = 32 and 8x + 6y = 38 →
  3. 3.9x + 6y = 21 and 6x + 9y = 24 →
  4. 4.3x − 6y = −51 and 5x − 3y = −36 →
  5. 5.6x + 3y = 30 and 6x + 6y = 54 →
  6. 6.3x − 6y = −21 and 2x − 6y = −30 →
  7. 7.2x − 2y = −4 and 5x + 4y = −73 →
  8. 8.3x + 5y = −27 and 5x + 3y = 3 →
  9. 9.2x − 2y = −14 and 6x − 4y = −30 →
  10. 10.3x + 5y = 23 and 5x + 3y = 1 →
  11. 11.7x + 2y = 40 and 2x + 7y = −40 →
  12. 12.x − 2y = 16 and 3x + 5y = 4 →
  13. 13.6x + 5y = 52 and x + 4y = 34 →
  14. 14.6x − 4y = −86 and x + 3y = 15 →
  15. 15.x + 3y = 12 and 2x − y = 17 →
  16. 16.x + 7y = 50 and 7x + y = 14 →
  17. 17.5x − 4y = 1 and x + y = 2 →
  18. 18.3x − 2y = −4 and 3x + 6y = 36 →
  19. 19.8x + 7y = −2 and 7x + 8y = 2 →
  20. 20.3x − 5y = −16 and 5x − 4y = 8 →
  21. 21.x − 6y = 8 and 2x + y = −10 →
  22. 22.x + y = 3 and 4x − 5y = −6 →
  23. 23.2x − 4y = −18 and 4x + 5y = 16 →
  24. 24.x − 3y = 21 and 5x + 2y = 20 →
  25. 25.7x + 6y = −69 and 6x + 7y = −61 →
  26. 26.4x − y = 24 and 3x − 2y = 8 →
  27. 27.4x + 2y = −12 and 4x + 3y = −8 →
  28. 28.8x + 5y = −52 and 5x + 8y = −13 →
  29. 29.7x + 5y = 61 and 5x + 7y = 71 →
  30. 30.2x + 2y = 6 and x − 4y = −7 →
  31. 31.4x + 2y = 54 and 6x + 5y = 99 →
  32. 32.3x + 5y = −18 and 3x − 2y = 24 →
  33. 33.5x + 6y = −16 and 2x + 5y = −22 →
  34. 34.x − 5y = 11 and 2x − 6y = 14 →
  35. 35.3x − 5y = 41 and 3x + 6y = −36 →
  36. 36.4x + 6y = 68 and 4x + 4y = 56 →
  37. 37.2x − 3y = −5 and 2x + y = 7 →
  38. 38.4x + 5y = 62 and 4x + 6y = 68 →
  39. 39.7x + 2y = −35 and 2x + 7y = 35 →
  40. 40.4x + 2y = −8 and x + 6y = 20 →

Answer key

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

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