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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 53 · 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 = −25 and 2x + 3y = −20 →
  2. 2.5x + 2y = 4 and 2x + 5y = −11 →
  3. 3.3x + 3y = 36 and 2x + 6y = 60 →
  4. 4.5x + 3y = 8 and 2x + 6y = 8 →
  5. 5.2x + 6y = −12 and 4x + 3y = −33 →
  6. 6.6x + 4y = −46 and 4x − 6y = −48 →
  7. 7.3x + 9y = 42 and 9x + 3y = −42 →
  8. 8.9x + 2y = −77 and 2x + 9y = 0 →
  9. 9.9x + 3y = 33 and 3x + 9y = 27 →
  10. 10.3x + 6y = −42 and 6x − 6y = −30 →
  11. 11.5x − 2y = 28 and 5x − 4y = 36 →
  12. 12.5x − 2y = 5 and 6x + 5y = 43 →
  13. 13.4x + 2y = −8 and 2x + 4y = 2 →
  14. 14.8x + 2y = −36 and 2x + 8y = 6 →
  15. 15.6x + y = −45 and 2x − 6y = 42 →
  16. 16.3x + 5y = 30 and 5x + 3y = 34 →
  17. 17.7x + 3y = −29 and 3x + 7y = 39 →
  18. 18.x + 5y = 7 and 2x + 6y = 10 →
  19. 19.3x + 5y = −51 and x − 4y = 34 →
  20. 20.6x + 2y = 8 and 2x + 6y = 8 →
  21. 21.3x + 6y = −15 and 6x + 3y = −3 →
  22. 22.2x − 2y = 4 and 4x + 2y = 2 →
  23. 23.6x + 3y = 9 and 3x + 4y = 7 →
  24. 24.5x − 4y = 2 and 5x + 6y = 22 →
  25. 25.x + 3y = 5 and 2x + y = −5 →
  26. 26.3x + 7y = −40 and 7x + 3y = 0 →
  27. 27.4x − 5y = −77 and 4x + 4y = 4 →
  28. 28.9x + 6y = −48 and 6x + 9y = −12 →
  29. 29.4x + 6y = 64 and 3x − 2y = 9 →
  30. 30.4x + 5y = 23 and 5x + 4y = 22 →
  31. 31.5x + 3y = −30 and 3x + 5y = −2 →
  32. 32.3x + 3y = 9 and x − 2y = 0 →
  33. 33.5x − y = −25 and 5x − 6y = −50 →
  34. 34.3x + 2y = −13 and 2x + 3y = −22 →
  35. 35.4x + 7y = −6 and 7x + 4y = 6 →
  36. 36.2x + 3y = −5 and 6x − 5y = 55 →
  37. 37.2x + 2y = 0 and 2x + 5y = 3 →
  38. 38.5x + y = −7 and 2x + y = 2 →
  39. 39.2x + 5y = 39 and 5x + 2y = 3 →
  40. 40.4x + y = 18 and x + 4y = 27 →

Answer key

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

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