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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 395 · 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. 1.6x − 6y = 12 and 2x − y = 5 →
  2. 2.x − 3y = 2 and 3x + 6y = 21 →
  3. 3.3x + y = −16 and 5x + y = −32 →
  4. 4.4x + 6y = −26 and x + y = −2 →
  5. 5.3x + 2y = 8 and 2x + 3y = 7 →
  6. 6.6x + 3y = −57 and 5x + y = −46 →
  7. 7.2x + y = 0 and x + y = −3 →
  8. 8.3x + 6y = 45 and 4x + 5y = 45 →
  9. 9.6x + 3y = 6 and x + 5y = 19 →
  10. 10.2x − 5y = −9 and 2x + 5y = 21 →
  11. 11.6x + 4y = 12 and 4x + 6y = −2 →
  12. 12.5x + y = 45 and x + 5y = 33 →
  13. 13.2x + 4y = −44 and 4x + 2y = −40 →
  14. 14.6x + 4y = 40 and 2x + 4y = 8 →
  15. 15.8x + 9y = −17 and 9x + 8y = 0 →
  16. 16.2x − 2y = 2 and x − 5y = −3 →
  17. 17.6x + 4y = 30 and 4x + 6y = 0 →
  18. 18.3x + 4y = −16 and 5x − 2y = 34 →
  19. 19.x + 7y = 54 and 7x + y = −54 →
  20. 20.5x + 3y = 31 and x + 2y = 9 →
  21. 21.9x + 3y = −9 and 3x + 9y = −75 →
  22. 22.8x + 7y = 50 and 7x + 8y = 55 →
  23. 23.6x + y = −22 and 4x − 4y = −24 →
  24. 24.5x + 3y = 54 and 6x + y = 44 →
  25. 25.x + y = −4 and 2x − 5y = −15 →
  26. 26.5x − 6y = 21 and x + 4y = −1 →
  27. 27.2x + 8y = 48 and 8x + 2y = 72 →
  28. 28.8x + 5y = −58 and 5x + 8y = −46 →
  29. 29.3x + 2y = −17 and 2x + 6y = −2 →
  30. 30.3x + 2y = −10 and 2x + 3y = −5 →
  31. 31.7x + y = −16 and x + 7y = 32 →
  32. 32.5x + 4y = 7 and 6x + 6y = 12 →
  33. 33.x + 4y = 34 and 3x + y = 25 →
  34. 34.4x − 2y = 42 and 5x − 3y = 57 →
  35. 35.8x + 3y = 34 and 3x + 8y = 54 →
  36. 36.5x + 4y = 18 and 6x + y = −5 →
  37. 37.5x + 4y = 36 and 4x + 5y = 36 →
  38. 38.3x + 4y = −23 and x + 6y = −45 →
  39. 39.3x + y = 29 and x + 3y = 15 →
  40. 40.x − 3y = −11 and 2x − 3y = −19 →

Answer key

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

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