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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 69 · 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. 1.3x + 2y = 23 and x − 6y = 21 →
  2. 2.6x + 4y = −20 and 2x + 6y = 12 →
  3. 3.5x + 8y = 23 and 8x + 5y = 29 →
  4. 4.3x + 5y = 33 and 5x + 3y = 23 →
  5. 5.5x + 3y = 19 and 5x + 5y = 25 →
  6. 6.3x + 5y = 16 and 5x + 3y = 32 →
  7. 7.5x − 4y = −26 and 6x + 6y = 66 →
  8. 8.x + y = 12 and 4x + y = 24 →
  9. 9.2x + 5y = 10 and x + y = −1 →
  10. 10.6x + y = 23 and 2x + y = 11 →
  11. 11.2x + y = 0 and x + 2y = 12 →
  12. 12.4x + 7y = 71 and 7x + 4y = 50 →
  13. 13.x + 2y = −6 and 3x − 6y = −6 →
  14. 14.3x + 6y = 21 and 5x − 5y = −85 →
  15. 15.2x + 3y = 11 and 3x + 2y = −1 →
  16. 16.5x + 4y = 23 and 4x + 5y = 22 →
  17. 17.4x − 6y = −66 and 4x + y = −3 →
  18. 18.2x + y = 19 and 5x + 5y = 70 →
  19. 19.3x + 2y = 7 and 6x + 6y = 0 →
  20. 20.3x + 2y = 9 and 4x + 5y = −2 →
  21. 21.3x + 2y = 17 and 2x + 3y = 8 →
  22. 22.2x + 7y = 36 and 7x + 2y = −9 →
  23. 23.5x + y = 3 and x + 5y = −9 →
  24. 24.4x + 6y = −32 and 5x − 2y = −2 →
  25. 25.3x + 7y = −41 and 7x + 3y = 11 →
  26. 26.6x + 2y = −30 and 5x − 5y = 15 →
  27. 27.x + 3y = −8 and 3x + y = −8 →
  28. 28.6x − 5y = −5 and x + y = 12 →
  29. 29.3x − 4y = −31 and 6x + 6y = 36 →
  30. 30.2x + 9y = −13 and 9x + 2y = 57 →
  31. 31.4x + 5y = −22 and 3x + 4y = −18 →
  32. 32.2x + 3y = 16 and 3x − 4y = −27 →
  33. 33.3x − 3y = 12 and x − 6y = −6 →
  34. 34.9x + y = 32 and x + 9y = −32 →
  35. 35.4x + 6y = 58 and 4x − 4y = −32 →
  36. 36.7x + 5y = −10 and 5x + 7y = −38 →
  37. 37.6x + 4y = 10 and x + 3y = −10 →
  38. 38.3x + 2y = 20 and 2x + 3y = 15 →
  39. 39.4x + y = −14 and x + 4y = −26 →
  40. 40.5x + 6y = 87 and 3x − 6y = −15 →

Answer key

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

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