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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 586 · 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 + 4y = 0 and x + y = 1 →
  2. 2.4x + 6y = −10 and 5x + 4y = −2 →
  3. 3.4x + 5y = 73 and 4x − 2y = 10 →
  4. 4.5x + 4y = 46 and 4x + 6y = 48 →
  5. 5.x + 3y = 6 and 3x + 2y = 11 →
  6. 6.2x − 4y = 20 and 4x − 2y = 4 →
  7. 7.7x + 8y = 9 and 8x + 7y = −9 →
  8. 8.x − 4y = 26 and x − 3y = 18 →
  9. 9.4x + 6y = 58 and 4x − y = 23 →
  10. 10.7x + y = 48 and x + 7y = 48 →
  11. 11.6x + 2y = 42 and 4x − 5y = 9 →
  12. 12.9x + 7y = −43 and 7x + 9y = −37 →
  13. 13.6x + 5y = −28 and 5x + 6y = −16 →
  14. 14.2x − 4y = 0 and 6x − y = 33 →
  15. 15.5x + y = 32 and x + 4y = 14 →
  16. 16.4x + 2y = −30 and 3x + 2y = −25 →
  17. 17.6x − 3y = 27 and 5x − 6y = 5 →
  18. 18.x + 2y = 5 and 5x + 5y = 20 →
  19. 19.7x + 2y = −55 and 2x + 7y = 10 →
  20. 20.6x + 3y = 63 and 3x + 6y = 72 →
  21. 21.x − 2y = −22 and 4x + 6y = 10 →
  22. 22.4x − y = 31 and 6x + 2y = 64 →
  23. 23.8x + y = 75 and x + 8y = 33 →
  24. 24.3x − 3y = 18 and x + 4y = 21 →
  25. 25.2x + 5y = 51 and 6x + y = 55 →
  26. 26.3x + 2y = 17 and x + y = 4 →
  27. 27.7x + 8y = −20 and 8x + 7y = −25 →
  28. 28.3x + 2y = −26 and 5x + 3y = −43 →
  29. 29.x + 5y = −4 and 6x + 3y = −51 →
  30. 30.4x − 3y = 6 and x + y = 12 →
  31. 31.2x − 2y = 18 and x + 2y = −3 →
  32. 32.2x + 7y = 62 and 7x + 2y = 37 →
  33. 33.6x + 4y = 90 and 4x + 6y = 90 →
  34. 34.4x + 3y = −13 and 3x + 4y = −15 →
  35. 35.3x + 5y = 3 and 5x + 2y = −33 →
  36. 36.2x + 5y = 32 and x + 6y = 30 →
  37. 37.8x + 3y = 90 and 3x + 8y = 75 →
  38. 38.3x + 7y = 22 and 7x + 3y = −2 →
  39. 39.6x + 4y = 32 and 3x + 4y = 14 →
  40. 40.2x − 2y = 14 and 5x + 2y = 49 →

Answer key

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

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