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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 940 · 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 = −22 and 2x + 4y = −18 →
  2. 2.4x − 5y = 2 and 4x − 6y = 0 →
  3. 3.5x − 6y = 4 and 5x + y = 11 →
  4. 4.3x + 5y = 32 and 3x − 6y = −45 →
  5. 5.6x + 7y = 13 and 7x + 6y = 13 →
  6. 6.5x + 3y = 11 and 4x + 5y = 14 →
  7. 7.2x + y = 6 and x + 2y = 15 →
  8. 8.2x + 2y = 16 and 3x + 5y = 36 →
  9. 9.2x + 2y = 14 and 5x + 2y = 23 →
  10. 10.6x + 3y = −72 and 4x + 6y = −72 →
  11. 11.7x + 4y = 25 and 4x + 7y = −14 →
  12. 12.x + 2y = 5 and 3x + 3y = 9 →
  13. 13.3x + 3y = 30 and 3x − y = 18 →
  14. 14.4x − 6y = −8 and 3x + 5y = 51 →
  15. 15.6x + 2y = 52 and 2x + 6y = 28 →
  16. 16.2x + 3y = 34 and 3x + 2y = 36 →
  17. 17.2x + 4y = −2 and 4x + y = 17 →
  18. 18.x + y = 11 and x − 5y = −7 →
  19. 19.5x + 3y = 11 and 3x − 3y = 45 →
  20. 20.8x + 6y = 104 and 6x + 8y = 106 →
  21. 21.3x − 5y = −36 and x + y = 12 →
  22. 22.5x + 6y = 14 and 4x − y = 17 →
  23. 23.4x + 4y = 20 and 2x + 5y = 34 →
  24. 24.3x + y = 0 and 4x − 3y = −26 →
  25. 25.x − 4y = 5 and x − 5y = 8 →
  26. 26.7x + 4y = 2 and 4x + 7y = 20 →
  27. 27.2x + 4y = 20 and x − y = 7 →
  28. 28.4x − 4y = 0 and x + 2y = 24 →
  29. 29.3x + 4y = 51 and x + 5y = 50 →
  30. 30.3x + 2y = 13 and 2x + 3y = 22 →
  31. 31.8x + 6y = 106 and 6x + 8y = 104 →
  32. 32.2x + 3y = 1 and 3x + 2y = 14 →
  33. 33.3x + 2y = 38 and 2x + 3y = 37 →
  34. 34.x + 6y = 50 and 6x + y = 20 →
  35. 35.4x + 8y = 28 and 8x + 4y = 32 →
  36. 36.8x + 9y = −90 and 9x + 8y = −97 →
  37. 37.2x + 5y = 6 and 3x + 2y = 20 →
  38. 38.x + 2y = 4 and 3x − 2y = −12 →
  39. 39.x + 5y = 17 and 4x + y = 11 →
  40. 40.4x + 2y = −8 and 2x + 2y = 4 →

Answer key

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

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