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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 175 · 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 + 2y = 8 and 3x + 3y = 18 →
  2. 2.2x + 3y = −1 and 4x + 5y = 3 →
  3. 3.x − 6y = −39 and x + 5y = 27 →
  4. 4.2x + 3y = 0 and 6x + y = −16 →
  5. 5.x − 3y = −22 and 6x − 5y = −67 →
  6. 6.9x + 3y = 12 and 3x + 9y = 60 →
  7. 7.8x + y = 21 and x + 8y = −21 →
  8. 8.6x + 7y = 9 and 7x + 6y = 4 →
  9. 9.4x + 4y = 8 and 2x + 3y = 5 →
  10. 10.5x + 3y = −2 and 2x + 6y = −20 →
  11. 11.6x + y = 42 and 3x + 6y = 54 →
  12. 12.8x + 5y = 83 and 5x + 8y = 86 →
  13. 13.6x + 4y = 52 and 5x + 6y = 46 →
  14. 14.2x − 3y = 10 and 4x − 3y = 8 →
  15. 15.2x + 6y = 50 and 6x + 2y = 38 →
  16. 16.x + 4y = −27 and 4x + y = −3 →
  17. 17.6x + 9y = −3 and 9x + 6y = −12 →
  18. 18.x + 3y = 19 and 6x + 2y = 2 →
  19. 19.6x − 5y = −69 and 3x − 3y = −36 →
  20. 20.2x + 9y = 71 and 9x + 2y = 50 →
  21. 21.2x + 3y = −6 and x − 3y = 24 →
  22. 22.4x + 5y = −38 and x + 4y = −26 →
  23. 23.x + 2y = −11 and 2x + y = 5 →
  24. 24.3x − 3y = 9 and 2x + 3y = −29 →
  25. 25.x + 4y = −29 and 4x + y = −11 →
  26. 26.4x − 4y = 0 and 3x + y = −4 →
  27. 27.3x + y = −30 and x + 3y = −26 →
  28. 28.5x − 4y = 24 and x − 2y = 6 →
  29. 29.4x − 5y = 24 and 6x + 5y = −14 →
  30. 30.6x + 5y = −4 and 6x − 6y = 84 →
  31. 31.x + 3y = 27 and 3x + 5y = 49 →
  32. 32.x + 3y = 19 and 3x + y = −15 →
  33. 33.4x + 5y = 47 and x + 4y = 31 →
  34. 34.x + 2y = 1 and 6x + 6y = 0 →
  35. 35.6x − 3y = 39 and x + 4y = −34 →
  36. 36.5x + 2y = 33 and 5x + 6y = 9 →
  37. 37.5x − 3y = −5 and 2x − 6y = 22 →
  38. 38.x + 6y = −4 and 5x + 2y = 36 →
  39. 39.4x + 2y = −18 and 4x + 5y = −3 →
  40. 40.x − 3y = 11 and 5x + 5y = −25 →

Answer key

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

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