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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 960 · 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.x + 5y = 13 and 3x − 2y = 5 →
  2. 2.2x + 4y = −20 and 4x + 2y = 8 →
  3. 3.x + 5y = 53 and 3x + y = 33 →
  4. 4.3x + 3y = 12 and 3x + 6y = 3 →
  5. 5.8x + 6y = 82 and 6x + 8y = 86 →
  6. 6.2x + 2y = 2 and 3x − 3y = 21 →
  7. 7.2x − 2y = 14 and 6x − 4y = 44 →
  8. 8.6x + 4y = −10 and 4x + 6y = 10 →
  9. 9.2x − 3y = 7 and 5x + 2y = 46 →
  10. 10.x + 9y = 20 and 9x + y = 20 →
  11. 11.x + 5y = −9 and 3x + 3y = 9 →
  12. 12.3x − 4y = 3 and 6x + 4y = 42 →
  13. 13.x − 2y = −10 and 3x + 3y = 33 →
  14. 14.9x + y = −22 and x + 9y = −38 →
  15. 15.8x + 3y = −70 and 3x + 8y = −40 →
  16. 16.x − 3y = −3 and 2x + y = 22 →
  17. 17.4x − 3y = 3 and 2x − 3y = −9 →
  18. 18.4x + 3y = 14 and 3x + 4y = 14 →
  19. 19.x + 4y = 27 and 6x − 5y = −12 →
  20. 20.6x − 2y = 26 and x + 3y = 31 →
  21. 21.x + y = −16 and 2x + 4y = −46 →
  22. 22.2x + 5y = 26 and 2x − 3y = 10 →
  23. 23.5x + 4y = −32 and x + 4y = −16 →
  24. 24.3x + 6y = −15 and 3x + y = 5 →
  25. 25.4x + y = 21 and 5x + 2y = 30 →
  26. 26.7x + 4y = 85 and 4x + 7y = 91 →
  27. 27.2x − 5y = −31 and 2x + 5y = 39 →
  28. 28.2x − 5y = −27 and 6x − 2y = −16 →
  29. 29.6x − 2y = 48 and 6x + y = 57 →
  30. 30.6x − y = −15 and 6x + 4y = 30 →
  31. 31.5x − 4y = 71 and x + 6y = −47 →
  32. 32.4x + 9y = −27 and 9x + 4y = 53 →
  33. 33.2x + 6y = 16 and x + y = 4 →
  34. 34.6x + 6y = 54 and 4x + y = 12 →
  35. 35.x + 2y = 19 and 2x + y = 11 →
  36. 36.x − y = 0 and 3x + y = 8 →
  37. 37.x + y = −2 and 6x − 2y = 28 →
  38. 38.2x + 5y = 9 and 2x − 2y = 2 →
  39. 39.x − 2y = 15 and x + 5y = −27 →
  40. 40.8x + 7y = 37 and 7x + 8y = 38 →

Answer key

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

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