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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 699 · 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. 1.6x − 4y = −12 and x + 5y = 32 →
  2. 2.8x + 2y = 34 and 2x + 8y = 46 →
  3. 3.4x − 2y = 0 and x + 4y = 18 →
  4. 4.3x + 5y = 11 and 4x − y = 30 →
  5. 5.x + 5y = 33 and 5x + y = 45 →
  6. 6.2x + y = −9 and x + 2y = −9 →
  7. 7.x + 8y = 60 and 8x + y = −24 →
  8. 8.3x − 3y = −18 and 3x + 6y = 9 →
  9. 9.4x + 3y = 27 and 3x + y = 24 →
  10. 10.6x + 3y = −24 and 3x + 6y = −3 →
  11. 11.6x + 6y = 30 and 6x + y = 45 →
  12. 12.2x + 4y = −32 and 4x + 2y = −34 →
  13. 13.5x + 4y = 52 and x − y = 5 →
  14. 14.5x − y = 11 and 5x − 2y = 17 →
  15. 15.3x + 6y = −27 and 4x + 3y = −26 →
  16. 16.3x + 4y = 31 and 4x + 3y = 32 →
  17. 17.2x − y = 2 and x + 6y = 53 →
  18. 18.5x − 5y = −55 and 2x + 2y = −14 →
  19. 19.3x + 6y = 69 and 4x − 2y = 2 →
  20. 20.9x + 6y = −69 and 6x + 9y = −36 →
  21. 21.8x + 9y = 99 and 9x + 8y = 105 →
  22. 22.3x − 2y = 20 and 6x + 3y = −9 →
  23. 23.x + 4y = 35 and 4x + y = 20 →
  24. 24.x + 6y = −4 and x − 4y = 6 →
  25. 25.x − y = 11 and 2x + 2y = −6 →
  26. 26.x + 3y = 29 and 3x + 2y = 38 →
  27. 27.6x + 4y = 70 and 4x − 4y = 20 →
  28. 28.5x + 9y = 93 and 9x + 5y = 89 →
  29. 29.6x − 2y = 12 and 5x + 6y = 56 →
  30. 30.6x + 2y = −4 and x − 2y = −3 →
  31. 31.x − 5y = −8 and x + 2y = 6 →
  32. 32.6x + 5y = −18 and 5x + 6y = −26 →
  33. 33.6x − 2y = −14 and 3x − 3y = −15 →
  34. 34.9x + 3y = 45 and 3x + 9y = −57 →
  35. 35.8x + 9y = −2 and 9x + 8y = 2 →
  36. 36.2x + y = 15 and x + 2y = 6 →
  37. 37.6x + y = −33 and 4x − 2y = −14 →
  38. 38.6x + y = 9 and x − 4y = −11 →
  39. 39.9x + 8y = 73 and 8x + 9y = 63 →
  40. 40.3x + 6y = 21 and 6x − 6y = −84 →

Answer key

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

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