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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 168 · 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. 1.4x + 2y = 8 and 5x + 3y = 11 →
  2. 2.4x + 2y = −4 and 2x + 4y = 22 →
  3. 3.2x + 3y = 19 and 3x + 2y = 26 →
  4. 4.4x − 2y = −16 and 2x + y = −24 →
  5. 5.8x + 2y = 40 and 2x + 8y = 70 →
  6. 6.x + 5y = 17 and 3x − 3y = 15 →
  7. 7.5x + 2y = 33 and 2x − 4y = −6 →
  8. 8.6x + 4y = 14 and 4x + 6y = 26 →
  9. 9.5x − 5y = −55 and 2x − 3y = −31 →
  10. 10.6x + 2y = 56 and 2x + 6y = 24 →
  11. 11.3x + 3y = 33 and 2x − 2y = −2 →
  12. 12.4x − 6y = −44 and 4x − 2y = −36 →
  13. 13.x + 4y = 4 and 4x + y = −29 →
  14. 14.x + 7y = 38 and 7x + y = 26 →
  15. 15.6x − 3y = 39 and 2x + y = 19 →
  16. 16.2x + 3y = 11 and 5x − 4y = −7 →
  17. 17.4x + 8y = 40 and 8x + 4y = 68 →
  18. 18.x − y = 4 and 2x + 3y = −2 →
  19. 19.3x + 5y = 49 and 4x + 5y = 52 →
  20. 20.7x + 4y = 43 and 4x + 7y = 34 →
  21. 21.x + 2y = 3 and 2x + y = 15 →
  22. 22.5x + 6y = −1 and 4x − 2y = 6 →
  23. 23.2x + 5y = 24 and 5x + 2y = 18 →
  24. 24.6x + 3y = −24 and 3x + 6y = −3 →
  25. 25.2x − 5y = −5 and 2x + y = 13 →
  26. 26.3x + 3y = −18 and 4x + 5y = −21 →
  27. 27.4x − 2y = 30 and 5x + 3y = 32 →
  28. 28.2x − 3y = −31 and 5x + 2y = −11 →
  29. 29.5x + 5y = −10 and 5x + y = −14 →
  30. 30.2x + 6y = −40 and 6x + 2y = −24 →
  31. 31.3x + y = 20 and 4x − 6y = −10 →
  32. 32.8x + y = 12 and x + 8y = 33 →
  33. 33.x + 4y = 19 and 2x + 3y = 23 →
  34. 34.6x + 4y = 10 and 4x + 6y = 20 →
  35. 35.5x − 4y = 52 and 2x + 4y = 4 →
  36. 36.4x + 2y = −6 and 5x + y = −9 →
  37. 37.3x + 9y = 78 and 9x + 3y = 66 →
  38. 38.4x + 2y = 20 and 5x + y = 19 →
  39. 39.3x + 4y = −6 and 4x + 3y = 6 →
  40. 40.2x + 5y = −8 and 5x + 2y = 1 →

Answer key

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

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