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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 730 · 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. 1.2x + 3y = 1 and 3x + 4y = 3 →
  2. 2.x + 4y = 45 and x + 2y = 27 →
  3. 3.4x + 4y = −24 and 2x + 5y = −6 →
  4. 4.2x + 3y = 7 and 4x − 2y = 22 →
  5. 5.3x + 6y = −6 and 6x − 2y = 44 →
  6. 6.2x + 2y = 12 and 2x + 4y = 18 →
  7. 7.8x + 2y = 24 and 2x + 8y = 66 →
  8. 8.4x − 2y = 2 and 4x + 6y = 26 →
  9. 9.6x + 6y = 30 and 2x + 5y = 19 →
  10. 10.6x + 2y = 38 and 2x + 6y = 50 →
  11. 11.8x + 9y = −15 and 9x + 8y = −19 →
  12. 12.5x + 5y = 25 and 5x + y = 9 →
  13. 13.2x + 4y = 12 and x − 6y = −2 →
  14. 14.9x + 7y = 89 and 7x + 9y = 87 →
  15. 15.3x + 7y = 15 and 7x + 3y = −5 →
  16. 16.x − 2y = −15 and 2x + y = 10 →
  17. 17.3x + 4y = −9 and 4x + 3y = −19 →
  18. 18.7x + 2y = 57 and 2x + 7y = 42 →
  19. 19.x + 5y = −53 and 5x + y = −49 →
  20. 20.x − 4y = −5 and x + 5y = 13 →
  21. 21.3x + 2y = 13 and x + 2y = 3 →
  22. 22.3x + y = −16 and x + 3y = 0 →
  23. 23.x + 5y = −12 and 5x + y = −36 →
  24. 24.2x − 2y = 6 and 2x + 4y = 30 →
  25. 25.4x + y = 31 and 4x − 4y = 56 →
  26. 26.2x + y = 14 and 5x − 2y = 53 →
  27. 27.x + 6y = 34 and 6x + y = −6 →
  28. 28.6x + 6y = 48 and x + 2y = 14 →
  29. 29.6x − y = 20 and x + 4y = 20 →
  30. 30.5x − 4y = 3 and 6x − 3y = 9 →
  31. 31.6x + 4y = −16 and 4x + 6y = −4 →
  32. 32.x + 2y = −22 and 4x + 3y = −53 →
  33. 33.4x + y = −39 and x + 4y = −36 →
  34. 34.2x + y = 5 and x + 4y = 27 →
  35. 35.2x + 2y = −8 and x + 5y = −16 →
  36. 36.6x + y = −23 and x + 6y = 2 →
  37. 37.6x + 9y = −6 and 9x + 6y = 21 →
  38. 38.4x + 3y = −41 and 2x − 2y = 4 →
  39. 39.2x + 3y = 29 and 2x − y = −7 →
  40. 40.5x + 6y = 8 and 5x + 2y = 16 →

Answer key

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

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