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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 992 · 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 − 3y = 5 and 4x + 3y = −25 →
  2. 2.9x + 8y = −7 and 8x + 9y = 7 →
  3. 3.5x + 2y = 14 and 2x + 5y = 14 →
  4. 4.3x + 4y = 50 and x + 4y = 38 →
  5. 5.x − 3y = 13 and 3x + y = 9 →
  6. 6.2x − 2y = 8 and 2x + 4y = 14 →
  7. 7.2x + 6y = −8 and 5x + 6y = 7 →
  8. 8.6x + 9y = 84 and 9x + 6y = 66 →
  9. 9.2x + 5y = 29 and x − 3y = −13 →
  10. 10.5x − 2y = 16 and 5x − 5y = 10 →
  11. 11.6x − y = 47 and 4x + 6y = 38 →
  12. 12.2x + 6y = 28 and x − 2y = −11 →
  13. 13.5x + 6y = 58 and 2x + y = 12 →
  14. 14.6x + 3y = −6 and 6x + 4y = −4 →
  15. 15.9x + 3y = 57 and 3x + 9y = −45 →
  16. 16.x + 2y = 11 and x − 5y = −3 →
  17. 17.4x + 8y = 36 and 8x + 4y = 48 →
  18. 18.2x + 3y = −3 and 3x + 2y = 3 →
  19. 19.x − y = 5 and 4x + 4y = −4 →
  20. 20.8x + 3y = −22 and 3x + 8y = −22 →
  21. 21.x + 9y = 53 and 9x + y = 77 →
  22. 22.x + 3y = 10 and 2x + 2y = 12 →
  23. 23.x + 2y = 19 and x + 4y = 29 →
  24. 24.x − y = 15 and x + y = −1 →
  25. 25.5x + 4y = 24 and 2x − 4y = 4 →
  26. 26.5x − y = −20 and 3x + 5y = 16 →
  27. 27.6x + 3y = 0 and x + 2y = −12 →
  28. 28.9x + 6y = 18 and 6x + 9y = 57 →
  29. 29.4x + y = 14 and x − y = 1 →
  30. 30.8x + 6y = 42 and 6x + 8y = 42 →
  31. 31.6x − y = 26 and 4x + y = 4 →
  32. 32.3x + 5y = 11 and 5x + 3y = 29 →
  33. 33.2x − 4y = 24 and 2x − 2y = 10 →
  34. 34.2x + 4y = 46 and 2x − y = 6 →
  35. 35.6x + 2y = 44 and 2x + 6y = 36 →
  36. 36.7x + 3y = 48 and 3x + 7y = 32 →
  37. 37.2x + 2y = 16 and 2x + 5y = 19 →
  38. 38.7x + y = 18 and x + 7y = −18 →
  39. 39.6x + y = −10 and 2x + 3y = 18 →
  40. 40.5x − 6y = 67 and 4x + 6y = −22 →

Answer key

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

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