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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 27 · 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 − y = −1 and 2x − 4y = −24 →
  2. 2.6x + 7y = −5 and 7x + 6y = 5 →
  3. 3.3x + 3y = 12 and 5x + y = 8 →
  4. 4.6x + 6y = −36 and 3x − 4y = 31 →
  5. 5.6x − 3y = 54 and 3x + 3y = 18 →
  6. 6.x − y = 0 and x − 5y = −32 →
  7. 7.3x − y = 32 and 4x + 2y = 16 →
  8. 8.2x − 5y = −8 and 2x + 6y = 14 →
  9. 9.2x + y = 25 and 6x + y = 61 →
  10. 10.6x − 4y = −8 and 3x + 6y = 60 →
  11. 11.x − y = 6 and 5x + 6y = 63 →
  12. 12.5x − 6y = −44 and 4x + 2y = 26 →
  13. 13.4x − 6y = 22 and 2x + 4y = −38 →
  14. 14.7x + 4y = −26 and 4x + 7y = −29 →
  15. 15.8x + 5y = 74 and 5x + 8y = 56 →
  16. 16.4x + 6y = 38 and 6x − 3y = 45 →
  17. 17.4x − 5y = 37 and x − y = 9 →
  18. 18.9x + 3y = 6 and 3x + 9y = 42 →
  19. 19.6x + 5y = −6 and 2x − 5y = 38 →
  20. 20.4x − 6y = 4 and x + 2y = 15 →
  21. 21.3x − 2y = 4 and 5x + 6y = 44 →
  22. 22.7x + y = 48 and x + 7y = 0 →
  23. 23.7x + 6y = −29 and 6x + 7y = −23 →
  24. 24.x + 6y = 33 and 6x − 4y = −82 →
  25. 25.x + 5y = −7 and 5x + y = 37 →
  26. 26.5x − 2y = 20 and 6x − 2y = 26 →
  27. 27.x + y = 3 and 5x − 5y = 75 →
  28. 28.6x + y = 0 and 3x − 4y = −27 →
  29. 29.5x + 2y = −10 and 2x + 2y = 2 →
  30. 30.8x + 5y = 15 and 5x + 8y = −15 →
  31. 31.x + y = −12 and x + 2y = −21 →
  32. 32.2x + 4y = −16 and x + 3y = −15 →
  33. 33.x + 8y = 13 and 8x + y = −22 →
  34. 34.7x + 2y = −3 and 2x + 7y = −33 →
  35. 35.8x + 5y = 55 and 5x + 8y = 49 →
  36. 36.5x − 2y = 33 and 5x − 3y = 37 →
  37. 37.3x + 9y = 75 and 9x + 3y = 81 →
  38. 38.x − 4y = 14 and 5x + 3y = −22 →
  39. 39.9x + 6y = 99 and 6x + 9y = 81 →
  40. 40.2x + y = 4 and 3x + y = 5 →

Answer key

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

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