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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 15 · 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 − 4y = 7 and 2x − 6y = 10 →
  2. 2.5x − 6y = 58 and 3x + 5y = 9 →
  3. 3.3x + 3y = −9 and 6x − 3y = 54 →
  4. 4.2x + y = 7 and 3x + 6y = 51 →
  5. 5.5x + 3y = −4 and 3x + 5y = −28 →
  6. 6.6x − 6y = −24 and 2x + 5y = 6 →
  7. 7.9x + 5y = 39 and 5x + 9y = 3 →
  8. 8.x − y = 2 and x − 6y = −18 →
  9. 9.x − 2y = 7 and 5x + 3y = −4 →
  10. 10.3x + 5y = −19 and 4x − 2y = −8 →
  11. 11.x + 5y = −18 and x − y = −6 →
  12. 12.2x + 5y = 57 and 6x + 2y = 54 →
  13. 13.6x + 5y = −22 and 4x − 3y = −40 →
  14. 14.9x + 7y = 126 and 7x + 9y = 130 →
  15. 15.2x + y = 5 and x − 5y = −3 →
  16. 16.8x + 3y = 41 and 3x + 8y = −19 →
  17. 17.8x + y = 51 and x + 8y = 30 →
  18. 18.x + 3y = 15 and x − y = 7 →
  19. 19.9x + 7y = 66 and 7x + 9y = 62 →
  20. 20.2x − 5y = 2 and 2x − 3y = 6 →
  21. 21.9x + 3y = −30 and 3x + 9y = −18 →
  22. 22.2x + 4y = 36 and 4x + 2y = 42 →
  23. 23.3x + 6y = 78 and 2x + 2y = 34 →
  24. 24.4x + 4y = 64 and x + 5y = 52 →
  25. 25.8x + y = −68 and x + 8y = −40 →
  26. 26.6x + 2y = 42 and 5x + y = 29 →
  27. 27.3x + 4y = 16 and 2x + 3y = 11 →
  28. 28.4x + 5y = −77 and 2x + 2y = −34 →
  29. 29.4x + 5y = 5 and 5x + 4y = 13 →
  30. 30.6x + y = 10 and x − y = 4 →
  31. 31.6x + y = −43 and x + 6y = −13 →
  32. 32.4x + 7y = 30 and 7x + 4y = 3 →
  33. 33.4x + 8y = 32 and 8x + 4y = 28 →
  34. 34.2x + 8y = 22 and 8x + 2y = −2 →
  35. 35.3x + 5y = −8 and 5x + 3y = −24 →
  36. 36.2x + y = 23 and 5x − 2y = 26 →
  37. 37.6x + 6y = 36 and x − 4y = −19 →
  38. 38.3x + 5y = −3 and 5x − 3y = 63 →
  39. 39.3x + 4y = 22 and 4x − 6y = −50 →
  40. 40.2x + 5y = −47 and 4x + 3y = −31 →

Answer key

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

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