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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 494 · 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 + y = 13 and x + 5y = 41 →
  2. 2.3x + 5y = −1 and 5x + 3y = 9 →
  3. 3.4x + 3y = 16 and 4x − 4y = −40 →
  4. 4.3x + 4y = −3 and 2x + 4y = −10 →
  5. 5.2x + 8y = 48 and 8x + 2y = −48 →
  6. 6.3x + 8y = −39 and 8x + 3y = 6 →
  7. 7.x + y = 2 and x + 4y = 11 →
  8. 8.4x + 2y = 10 and 6x − 5y = 7 →
  9. 9.2x + 4y = 24 and 2x + 6y = 40 →
  10. 10.6x + 3y = −24 and 3x + 6y = −39 →
  11. 11.6x + 8y = −62 and 8x + 6y = −78 →
  12. 12.3x + 4y = −54 and 4x + 3y = −51 →
  13. 13.x + y = 6 and 3x + 5y = 32 →
  14. 14.5x + 3y = 8 and 4x + 4y = 16 →
  15. 15.2x − y = −2 and 4x + y = 8 →
  16. 16.5x + 2y = 29 and 4x + 2y = 22 →
  17. 17.3x + 3y = −9 and 4x − y = −17 →
  18. 18.6x + 5y = −47 and 5x + 6y = −52 →
  19. 19.4x + 2y = 24 and x + 5y = −21 →
  20. 20.3x + 3y = −3 and 6x − 4y = −26 →
  21. 21.7x + 5y = 33 and 5x + 7y = 51 →
  22. 22.3x + y = 5 and 5x − 3y = 41 →
  23. 23.2x + 6y = −32 and 6x + 2y = 0 →
  24. 24.6x + y = −62 and x + 6y = −57 →
  25. 25.3x + 2y = −15 and 5x − 6y = −81 →
  26. 26.5x + 5y = 50 and 6x − 5y = 27 →
  27. 27.2x − y = 13 and 6x + 3y = 69 →
  28. 28.2x + 5y = 18 and 5x + 4y = 28 →
  29. 29.7x + 2y = −44 and 2x + 7y = −64 →
  30. 30.5x − y = 7 and 3x + 3y = 15 →
  31. 31.6x + 5y = −1 and 5x + 6y = −10 →
  32. 32.2x + y = 0 and 6x − 6y = −54 →
  33. 33.2x + y = 20 and x + 2y = 19 →
  34. 34.2x + 8y = 30 and 8x + 2y = −30 →
  35. 35.7x + 8y = 71 and 8x + 7y = 79 →
  36. 36.6x + 7y = 22 and 7x + 6y = 17 →
  37. 37.x + 8y = 9 and 8x + y = 9 →
  38. 38.8x + 2y = 54 and 2x + 8y = −54 →
  39. 39.7x + 2y = −9 and 2x + 7y = −9 →
  40. 40.4x + 5y = −26 and 2x − 3y = −24 →

Answer key

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

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