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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 796 · 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. 1.5x − 3y = −14 and 5x + 4y = −28 →
  2. 2.3x + 7y = −60 and 7x + 3y = −60 →
  3. 3.4x − y = −26 and 6x − 4y = −44 →
  4. 4.4x + 2y = 8 and 2x + 4y = 10 →
  5. 5.2x + 4y = −26 and 3x + 3y = −12 →
  6. 6.2x + 5y = −8 and 5x + 2y = −41 →
  7. 7.4x + 3y = 31 and 4x + 2y = 26 →
  8. 8.3x − 2y = 19 and 2x + 3y = 30 →
  9. 9.4x + y = −23 and 2x − 6y = −70 →
  10. 10.5x + 4y = 47 and 3x + 4y = 33 →
  11. 11.6x + 3y = 57 and 6x − 5y = 1 →
  12. 12.3x + y = −25 and 2x + y = −16 →
  13. 13.8x + 2y = −50 and 2x + 8y = 10 →
  14. 14.x + 5y = 2 and 2x + 6y = 8 →
  15. 15.3x + 5y = −12 and 2x + 2y = 0 →
  16. 16.x + 5y = 26 and 4x − 2y = −50 →
  17. 17.3x + 2y = −3 and 2x + 2y = 4 →
  18. 18.3x + 5y = 4 and 2x − y = −19 →
  19. 19.5x + y = 31 and 5x − y = 19 →
  20. 20.4x + 5y = −15 and 5x + 4y = −21 →
  21. 21.x − 2y = −8 and 2x − 3y = −15 →
  22. 22.2x + 2y = 14 and 6x + y = 32 →
  23. 23.2x + 4y = 34 and 3x + y = 21 →
  24. 24.6x + 7y = −103 and 7x + 6y = −105 →
  25. 25.4x + 5y = 34 and 6x + 3y = 24 →
  26. 26.x − y = 4 and 4x − 2y = 22 →
  27. 27.2x + 6y = −38 and 5x + 6y = −14 →
  28. 28.4x + 2y = 10 and 2x − 4y = 20 →
  29. 29.7x + 5y = 31 and 5x + 7y = 29 →
  30. 30.x + 4y = −19 and 3x + 5y = −29 →
  31. 31.2x + 5y = 27 and 2x + 2y = 0 →
  32. 32.6x + y = 55 and 5x + 2y = 47 →
  33. 33.4x + 3y = 49 and 3x + 4y = 49 →
  34. 34.3x − 2y = −36 and 6x + 4y = 0 →
  35. 35.8x + 2y = −74 and 2x + 8y = −56 →
  36. 36.5x + 2y = 3 and 5x − 5y = 10 →
  37. 37.x + y = 9 and 5x + y = 41 →
  38. 38.4x + 4y = 24 and 2x + 4y = 18 →
  39. 39.6x − 2y = 60 and x − 3y = 18 →
  40. 40.2x + 3y = −13 and 3x + 2y = −2 →

Answer key

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

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