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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 616 · 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 + y = −1 and 3x + y = −4 →
  2. 2.2x + 5y = −37 and 5x + 4y = −16 →
  3. 3.2x + y = 15 and 3x − 5y = 3 →
  4. 4.2x + 6y = 22 and 6x + 3y = 36 →
  5. 5.3x + 4y = −8 and x + 5y = 12 →
  6. 6.3x − 3y = −18 and 3x + 2y = 27 →
  7. 7.5x − 3y = 17 and 6x − 3y = 24 →
  8. 8.7x + 4y = 68 and 4x + 7y = 53 →
  9. 9.4x + 2y = 2 and 2x + 4y = −8 →
  10. 10.3x + y = 5 and 6x − y = −14 →
  11. 11.2x − 5y = 12 and 4x + 4y = −4 →
  12. 12.x + 5y = 46 and 4x − 4y = −32 →
  13. 13.6x + 9y = −45 and 9x + 6y = −15 →
  14. 14.9x + 3y = 27 and 3x + 9y = 57 →
  15. 15.x + 2y = −5 and 2x − 5y = −19 →
  16. 16.4x + 2y = 12 and 6x + 4y = 22 →
  17. 17.5x + 3y = −7 and x − y = 5 →
  18. 18.3x + y = −10 and 2x + 2y = 0 →
  19. 19.x − 3y = −20 and 4x + 4y = 32 →
  20. 20.4x + 4y = −12 and x + 4y = 0 →
  21. 21.3x + 4y = 18 and x − y = −8 →
  22. 22.3x + y = −13 and x + 3y = −23 →
  23. 23.3x + 6y = 21 and 6x − 5y = 25 →
  24. 24.2x + 3y = 8 and 4x − 6y = −8 →
  25. 25.3x + 4y = 19 and 5x + 4y = 29 →
  26. 26.3x + 2y = 25 and 5x + 3y = 41 →
  27. 27.5x + 2y = 23 and 3x + 3y = 21 →
  28. 28.6x + 6y = 60 and 3x + 2y = 28 →
  29. 29.x + 4y = −11 and 5x + 4y = −23 →
  30. 30.2x + 5y = 35 and 6x + 6y = 24 →
  31. 31.6x + 3y = −30 and 5x − 4y = −12 →
  32. 32.4x + 3y = 17 and 3x + 4y = 11 →
  33. 33.7x + 8y = −121 and 8x + 7y = −119 →
  34. 34.6x + 3y = 36 and 2x − 2y = −12 →
  35. 35.6x + 2y = −12 and 2x + 6y = 44 →
  36. 36.6x + 5y = 28 and x − 2y = 16 →
  37. 37.2x + 6y = 38 and 6x + y = −22 →
  38. 38.6x + 8y = 72 and 8x + 6y = 82 →
  39. 39.6x + 5y = 22 and 3x + 4y = 14 →
  40. 40.4x − 4y = −20 and 5x + 4y = 29 →

Answer key

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

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