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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 662 · 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.x − 6y = −32 and 4x − 5y = −52 →
  2. 2.x + 5y = 16 and x + y = 4 →
  3. 3.x + 4y = 24 and 5x + 3y = −16 →
  4. 4.5x + y = 30 and 3x + 4y = 1 →
  5. 5.3x − 2y = −16 and 5x − 4y = −30 →
  6. 6.5x + 6y = −2 and x − 5y = −19 →
  7. 7.5x − 3y = 23 and 2x + 6y = 2 →
  8. 8.3x + 4y = 17 and 4x + 3y = 18 →
  9. 9.5x + 6y = −26 and x + 2y = −10 →
  10. 10.4x + 7y = 17 and 7x + 4y = 5 →
  11. 11.5x + 3y = −4 and 3x + 5y = 4 →
  12. 12.9x + 3y = −36 and 3x + 9y = 60 →
  13. 13.6x − 6y = −30 and 4x + 2y = 22 →
  14. 14.9x + 4y = −45 and 4x + 9y = 45 →
  15. 15.5x + y = −32 and x − 5y = 4 →
  16. 16.2x + y = 6 and x + 2y = −3 →
  17. 17.2x + y = −1 and x + 5y = −32 →
  18. 18.4x + y = −1 and 4x − 6y = −22 →
  19. 19.9x + 5y = 37 and 5x + 9y = −23 →
  20. 20.5x + y = 16 and x − 4y = 41 →
  21. 21.8x + 2y = 72 and 2x + 8y = 48 →
  22. 22.2x − 4y = 30 and 3x − y = 25 →
  23. 23.3x + y = 12 and 4x − 4y = −16 →
  24. 24.x + 6y = 18 and 6x + y = 38 →
  25. 25.5x + 2y = 24 and 2x + 5y = 39 →
  26. 26.5x + 4y = 54 and 4x + 5y = 54 →
  27. 27.x + 6y = 29 and 2x + 3y = 4 →
  28. 28.2x + y = 25 and 6x + 6y = 96 →
  29. 29.4x + 3y = −2 and 3x + 4y = 2 →
  30. 30.4x + 8y = −80 and 8x + 4y = −64 →
  31. 31.x + 9y = −46 and 9x + y = −14 →
  32. 32.6x + 5y = −16 and x + 5y = −36 →
  33. 33.x − 5y = −36 and 4x − 2y = 18 →
  34. 34.3x + 2y = −3 and 2x + 3y = 3 →
  35. 35.4x − 2y = 16 and 4x − y = 10 →
  36. 36.x + y = 4 and x − 3y = −8 →
  37. 37.6x + 3y = 54 and 3x + 6y = 54 →
  38. 38.8x + 4y = 44 and 4x + 8y = 28 →
  39. 39.8x + 6y = 70 and 6x + 8y = 84 →
  40. 40.x + 6y = −28 and 6x + 6y = −18 →

Answer key

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

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