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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 797 · 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 + 2y = −16 and x + 6y = −53 →
  2. 2.x − 2y = −12 and 4x + 5y = −22 →
  3. 3.9x + 6y = 123 and 6x + 9y = 117 →
  4. 4.x − 4y = 28 and 4x − 3y = 47 →
  5. 5.4x − 5y = −25 and 6x + 3y = −27 →
  6. 6.x + 3y = 28 and 6x + 5y = 77 →
  7. 7.4x + 5y = 69 and 5x + 4y = 66 →
  8. 8.6x − 2y = 38 and x + 2y = 18 →
  9. 9.x + 3y = 29 and 5x + 3y = 61 →
  10. 10.3x − 3y = −3 and 3x − 2y = −4 →
  11. 11.4x + y = 6 and 6x − 3y = 18 →
  12. 12.x − 2y = −15 and x + 6y = 25 →
  13. 13.2x − 5y = 43 and 6x + 3y = 3 →
  14. 14.x − 2y = −11 and x + 3y = 24 →
  15. 15.5x + 6y = 33 and 2x − 5y = −9 →
  16. 16.8x + 7y = 3 and 7x + 8y = −3 →
  17. 17.6x + 3y = 9 and 5x + 2y = 4 →
  18. 18.x + y = 9 and 3x + 5y = 31 →
  19. 19.3x + y = 33 and 4x − 5y = 6 →
  20. 20.9x + 3y = 24 and 3x + 9y = −48 →
  21. 21.2x + 6y = −62 and 6x + 2y = −42 →
  22. 22.2x + 5y = 24 and 5x + 2y = 18 →
  23. 23.x − 4y = −30 and 4x + 6y = 34 →
  24. 24.5x − 2y = 26 and 5x + y = 47 →
  25. 25.5x + 9y = 79 and 9x + 5y = 75 →
  26. 26.9x + 2y = −7 and 2x + 9y = −70 →
  27. 27.x + 4y = −11 and 4x + y = 1 →
  28. 28.2x − 3y = −21 and 3x + 6y = 0 →
  29. 29.x − 5y = 17 and 3x − 4y = −4 →
  30. 30.4x + 6y = 14 and 3x + 4y = 11 →
  31. 31.9x + 3y = 12 and 3x + 9y = 12 →
  32. 32.5x + y = 42 and 3x − y = 22 →
  33. 33.2x + 3y = −24 and 5x + y = −47 →
  34. 34.x + 2y = 1 and x + 6y = 5 →
  35. 35.6x − 5y = −17 and 6x + 5y = −7 →
  36. 36.x + 3y = 6 and 5x − y = 46 →
  37. 37.4x − 3y = −21 and 3x + 5y = −23 →
  38. 38.3x − 5y = −11 and 5x + 6y = 39 →
  39. 39.5x + 5y = −15 and 6x − y = 10 →
  40. 40.8x + y = −64 and x + 8y = −71 →

Answer key

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

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