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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 795 · 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.x + 5y = −7 and 5x + 5y = −15 →
  2. 2.5x + 6y = 29 and x + 6y = 25 →
  3. 3.6x + 4y = 0 and 2x + 4y = 16 →
  4. 4.4x + 6y = 42 and 6x − 4y = −2 →
  5. 5.x + y = 9 and x − 3y = −19 →
  6. 6.7x + 2y = 50 and 2x + 7y = 40 →
  7. 7.4x − 4y = −40 and 6x − 5y = −56 →
  8. 8.6x − 6y = −66 and 2x + y = −10 →
  9. 9.2x + 3y = 24 and 4x − 4y = −12 →
  10. 10.4x + 3y = 40 and 6x + 4y = 56 →
  11. 11.9x + y = 61 and x + 9y = 69 →
  12. 12.x + 5y = 41 and x + y = 13 →
  13. 13.6x + 7y = −74 and 7x + 6y = −69 →
  14. 14.5x + 3y = −8 and 3x + 5y = −24 →
  15. 15.3x − 5y = −18 and 2x + 6y = 72 →
  16. 16.6x − 4y = 58 and x − 5y = 14 →
  17. 17.2x − 2y = 22 and 5x + 4y = 1 →
  18. 18.x + 2y = 10 and 2x + y = 11 →
  19. 19.2x + 4y = 18 and 3x + 4y = 25 →
  20. 20.x − 2y = −4 and x + 4y = 2 →
  21. 21.7x + y = 37 and x + 7y = −29 →
  22. 22.5x + y = 7 and 2x + 2y = 6 →
  23. 23.3x + 2y = 33 and 5x − 6y = −29 →
  24. 24.2x − y = 3 and 4x + 2y = 2 →
  25. 25.3x + 4y = 30 and 4x − 2y = 18 →
  26. 26.x − 3y = 1 and 2x + 4y = 22 →
  27. 27.8x + 2y = 50 and 2x + 8y = 80 →
  28. 28.2x + 4y = 6 and 4x + 2y = 18 →
  29. 29.4x + 6y = −68 and 2x + 4y = −42 →
  30. 30.2x − y = 11 and 2x − 2y = 4 →
  31. 31.4x − 6y = −32 and 2x + 4y = −2 →
  32. 32.4x + 9y = −2 and 9x + 4y = −37 →
  33. 33.x + 4y = 1 and 4x − 3y = 23 →
  34. 34.5x + 2y = −8 and 2x + 5y = −41 →
  35. 35.2x + 2y = −26 and x − 3y = 23 →
  36. 36.x + 5y = 11 and 2x + 2y = 14 →
  37. 37.6x + 2y = 24 and 2x + 6y = −24 →
  38. 38.5x + 4y = 2 and 3x + 5y = 9 →
  39. 39.4x − 2y = −2 and 4x + 3y = −7 →
  40. 40.2x + 3y = −5 and 3x − 5y = −17 →

Answer key

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

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