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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 256 · 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 − 2y = 4 and 5x + 2y = 41 →
  2. 2.6x − 6y = 12 and 5x − 4y = 13 →
  3. 3.x − y = 3 and 3x + 3y = 3 →
  4. 4.9x + 7y = −52 and 7x + 9y = −44 →
  5. 5.3x + y = 5 and x + 3y = 23 →
  6. 6.3x + y = 16 and 2x − y = 4 →
  7. 7.6x + 4y = −30 and 6x + 3y = −27 →
  8. 8.4x − 2y = −14 and x + y = −8 →
  9. 9.x + y = 3 and 3x − 3y = 3 →
  10. 10.9x + 3y = 45 and 3x + 9y = 87 →
  11. 11.4x + y = 36 and x − y = −1 →
  12. 12.6x + 3y = 36 and x − y = 0 →
  13. 13.4x + y = −16 and 4x + 6y = 24 →
  14. 14.6x − 2y = 0 and 6x + 4y = 54 →
  15. 15.x + 4y = 25 and 3x + 3y = 39 →
  16. 16.3x + 4y = −7 and 4x + 3y = 0 →
  17. 17.6x + 2y = −12 and x − 5y = 46 →
  18. 18.4x + 2y = 40 and 4x − 3y = 20 →
  19. 19.3x + 4y = 38 and 6x + 5y = 52 →
  20. 20.3x + 2y = 30 and 6x − 4y = 36 →
  21. 21.2x + y = 15 and 5x + 2y = 37 →
  22. 22.5x + 4y = 71 and 6x + 3y = 69 →
  23. 23.4x − 5y = 46 and 2x + 5y = 8 →
  24. 24.5x + 3y = 21 and 3x + 5y = 19 →
  25. 25.x − 4y = −16 and 4x + y = 21 →
  26. 26.3x + 2y = 22 and 2x + 3y = 23 →
  27. 27.2x − 5y = 22 and 4x + 2y = −4 →
  28. 28.4x + 4y = 44 and x − y = −5 →
  29. 29.4x + y = 0 and x + 4y = −15 →
  30. 30.6x − 2y = −52 and 6x + y = −37 →
  31. 31.2x + y = 3 and 3x + 6y = 0 →
  32. 32.3x + 5y = −7 and 5x + 6y = 0 →
  33. 33.x + 2y = 13 and 4x + 2y = 28 →
  34. 34.6x + 2y = 36 and x + 2y = 21 →
  35. 35.2x + 2y = 24 and 4x + 2y = 34 →
  36. 36.7x + y = 44 and x + 7y = 20 →
  37. 37.6x + 4y = 52 and 4x + 4y = 44 →
  38. 38.3x + 3y = −9 and 2x − 2y = −22 →
  39. 39.3x + 7y = 39 and 7x + 3y = 11 →
  40. 40.x + y = 11 and x − 3y = −5 →

Answer key

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

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