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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 443 · 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 = 19 and 5x + y = 23 →
  2. 2.x + 2y = 6 and 6x + 4y = −4 →
  3. 3.3x + 8y = −28 and 8x + 3y = −38 →
  4. 4.8x + y = 29 and x + 8y = 43 →
  5. 5.2x − 2y = −26 and x − 5y = −49 →
  6. 6.x + 4y = −9 and 4x + y = −21 →
  7. 7.8x + 4y = 52 and 4x + 8y = 68 →
  8. 8.4x + y = 17 and 3x − y = 11 →
  9. 9.6x + 3y = −6 and 4x − y = −16 →
  10. 10.6x + 8y = 18 and 8x + 6y = 10 →
  11. 11.x + 3y = 13 and 2x + 3y = 14 →
  12. 12.5x + 2y = 11 and x + 5y = 16 →
  13. 13.3x − 5y = 16 and 5x + 6y = −45 →
  14. 14.4x − 3y = 5 and x − y = 3 →
  15. 15.3x + 3y = 9 and 2x + y = 5 →
  16. 16.3x + 6y = −15 and 6x + 3y = −3 →
  17. 17.4x − 3y = −47 and 2x − 6y = −46 →
  18. 18.x + 7y = 10 and 7x + y = 22 →
  19. 19.4x + 4y = 12 and 5x + 4y = 19 →
  20. 20.2x − 5y = 20 and 4x + 2y = 16 →
  21. 21.3x + y = 28 and x + 3y = 28 →
  22. 22.2x + 4y = −14 and 4x + 2y = 2 →
  23. 23.4x + 6y = 36 and 4x + y = 16 →
  24. 24.4x − 3y = −45 and 3x + 2y = −21 →
  25. 25.2x + 6y = 32 and 6x + 2y = 48 →
  26. 26.2x + 7y = 38 and 7x + 2y = −47 →
  27. 27.x + 8y = 70 and 8x + y = −7 →
  28. 28.4x − y = 23 and 5x − 4y = 15 →
  29. 29.2x + 2y = 8 and 3x + y = −6 →
  30. 30.5x + 9y = 72 and 9x + 5y = 96 →
  31. 31.8x + 4y = 80 and 4x + 8y = 52 →
  32. 32.3x − 2y = 9 and 2x − 6y = 20 →
  33. 33.2x − 4y = 0 and 5x + 3y = 13 →
  34. 34.5x + y = 2 and x + 5y = 34 →
  35. 35.7x + 9y = 8 and 9x + 7y = −8 →
  36. 36.2x + 4y = 42 and 2x + 2y = 24 →
  37. 37.3x + 4y = 17 and x + 5y = 24 →
  38. 38.6x + 3y = 72 and 3x + 6y = 72 →
  39. 39.4x + 9y = 2 and 9x + 4y = −28 →
  40. 40.8x + 9y = 135 and 9x + 8y = 137 →

Answer key

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

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