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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 427 · 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. 1.6x − 5y = 55 and x − 3y = 20 →
  2. 2.4x + 2y = 14 and 2x + 4y = 4 →
  3. 3.6x + 8y = 16 and 8x + 6y = 40 →
  4. 4.4x + 9y = 6 and 9x + 4y = −19 →
  5. 5.3x + 9y = −51 and 9x + 3y = 39 →
  6. 6.4x + 4y = −24 and 2x + 4y = −10 →
  7. 7.6x + 6y = 12 and 6x + 2y = −16 →
  8. 8.9x + 7y = 16 and 7x + 9y = 16 →
  9. 9.x + 3y = 11 and 5x − 6y = −8 →
  10. 10.6x + 2y = 46 and 2x + 6y = −6 →
  11. 11.4x − 3y = 12 and 2x − 3y = 0 →
  12. 12.5x + 4y = −23 and 4x + 6y = −10 →
  13. 13.2x + 9y = 6 and 9x + 2y = −50 →
  14. 14.6x + 4y = 22 and 4x + 6y = 38 →
  15. 15.3x + 2y = 36 and 2x + 3y = 39 →
  16. 16.x + y = 2 and 6x − y = −16 →
  17. 17.2x − y = −16 and 5x + 4y = −14 →
  18. 18.4x + 5y = 19 and x + 4y = 13 →
  19. 19.6x + 3y = −27 and x + y = 0 →
  20. 20.2x + 3y = 11 and 5x + 5y = 30 →
  21. 21.x + 6y = 7 and 2x − 6y = −4 →
  22. 22.2x + 2y = 16 and 6x + y = 18 →
  23. 23.5x + 6y = −6 and 6x + y = −32 →
  24. 24.9x + 7y = −67 and 7x + 9y = −45 →
  25. 25.x − 4y = 32 and 3x + 4y = 0 →
  26. 26.2x + 4y = −8 and x − 3y = 1 →
  27. 27.6x + 2y = −8 and 5x + 5y = 20 →
  28. 28.5x + 2y = −31 and 3x + 5y = −30 →
  29. 29.x + 5y = 46 and 4x − 3y = −23 →
  30. 30.6x + 3y = 57 and 6x + y = 47 →
  31. 31.x − 2y = −20 and 4x + 5y = 37 →
  32. 32.5x + 3y = −12 and x − 5y = −36 →
  33. 33.x + y = 7 and x + 5y = 23 →
  34. 34.6x − 6y = −90 and 3x + 4y = 11 →
  35. 35.4x + 3y = 41 and 6x + y = 51 →
  36. 36.6x − y = −9 and 2x − 2y = 2 →
  37. 37.4x − y = 2 and 4x + 3y = 26 →
  38. 38.5x − 4y = 69 and x − 2y = 21 →
  39. 39.4x + 5y = 81 and x − 2y = −9 →
  40. 40.2x + 2y = 2 and 6x + 5y = 0 →

Answer key

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

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