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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 812 · 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 + 4y = −14 and 4x + 3y = −14 →
  2. 2.2x + y = −1 and 2x − 3y = 11 →
  3. 3.8x + 9y = −36 and 9x + 8y = −49 →
  4. 4.2x + 6y = −8 and x − 5y = −12 →
  5. 5.x − 2y = −12 and 4x + 5y = 43 →
  6. 6.9x + 7y = 119 and 7x + 9y = 121 →
  7. 7.2x + 4y = 8 and 4x + 2y = 10 →
  8. 8.3x + 5y = 11 and 2x + 4y = 10 →
  9. 9.4x + 4y = 32 and 3x − 6y = −39 →
  10. 10.8x + 2y = 68 and 2x + 8y = 62 →
  11. 11.2x + 5y = 53 and 5x + 2y = 59 →
  12. 12.4x − y = −23 and 5x + y = −31 →
  13. 13.4x + y = −34 and 2x + 6y = −6 →
  14. 14.4x + 6y = 54 and 3x + 5y = 42 →
  15. 15.3x + 3y = 12 and x − 2y = 10 →
  16. 16.2x + 9y = −9 and 9x + 2y = −79 →
  17. 17.x + 2y = 10 and 3x − 2y = −2 →
  18. 18.5x + 4y = −16 and 4x + 5y = −11 →
  19. 19.2x + 9y = −41 and 9x + 2y = 8 →
  20. 20.x + 3y = 9 and 4x − 6y = −72 →
  21. 21.6x − y = 38 and 4x + 6y = −28 →
  22. 22.5x − y = 11 and x + 2y = 22 →
  23. 23.x − 2y = −6 and x + 4y = 36 →
  24. 24.2x − 2y = 0 and x + 3y = 12 →
  25. 25.5x + 3y = 37 and 3x + 5y = 51 →
  26. 26.3x − 5y = 22 and 4x − y = 35 →
  27. 27.3x + y = 11 and x + 3y = 9 →
  28. 28.5x + y = −18 and 4x + 2y = −24 →
  29. 29.4x − 5y = −17 and x − 2y = −2 →
  30. 30.3x + 6y = 63 and 2x + y = 24 →
  31. 31.7x + 3y = −29 and 3x + 7y = −1 →
  32. 32.6x + 5y = 38 and 5x + 5y = 30 →
  33. 33.4x + 6y = −74 and 4x − y = −11 →
  34. 34.2x + 4y = −4 and 4x + 2y = −26 →
  35. 35.x + 4y = 34 and 4x + y = 16 →
  36. 36.6x + 6y = 30 and 2x − 6y = 34 →
  37. 37.2x + 5y = 9 and x − 3y = −1 →
  38. 38.3x + 4y = −4 and 2x + 6y = −16 →
  39. 39.x − 6y = −15 and 5x + y = 49 →
  40. 40.2x + 3y = 3 and 3x + 2y = 12 →

Answer key

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

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