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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 5 · 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. 1.7x + y = −54 and x + 7y = 6 →
  2. 2.3x − 5y = −26 and x + 4y = 31 →
  3. 3.5x + y = 7 and x + 5y = 11 →
  4. 4.2x − 2y = 2 and x − 5y = −3 →
  5. 5.6x − 2y = 44 and 3x + 2y = 28 →
  6. 6.2x + y = −4 and x + 4y = 19 →
  7. 7.5x + 6y = −33 and 3x − 3y = −33 →
  8. 8.x + y = 0 and 4x − 5y = −27 →
  9. 9.6x − 4y = 86 and 4x − 2y = 52 →
  10. 10.5x + 6y = −27 and 6x + 5y = −17 →
  11. 11.6x + 6y = −78 and 4x + 3y = −46 →
  12. 12.4x + 4y = −44 and 5x + 3y = −51 →
  13. 13.4x + 7y = 59 and 7x + 4y = 62 →
  14. 14.4x + y = −18 and 3x + 2y = −11 →
  15. 15.5x + 7y = 34 and 7x + 5y = 38 →
  16. 16.4x − y = −32 and x − 2y = −15 →
  17. 17.6x + 2y = −38 and 4x − 3y = −21 →
  18. 18.9x + 6y = −33 and 6x + 9y = −57 →
  19. 19.2x + 5y = 12 and 5x + 2y = 9 →
  20. 20.x + 6y = −9 and 5x + 3y = −18 →
  21. 21.4x + 4y = 12 and 2x + y = 10 →
  22. 22.4x − 2y = −4 and 5x + y = −26 →
  23. 23.6x + 5y = 21 and 5x + 4y = 17 →
  24. 24.6x + y = −33 and x + y = −3 →
  25. 25.x − 5y = −34 and x + 4y = 38 →
  26. 26.2x + 8y = 44 and 8x + 2y = 56 →
  27. 27.4x + 3y = 11 and 3x + 4y = 3 →
  28. 28.x − y = 5 and 5x + 6y = 58 →
  29. 29.6x − 3y = 12 and x + 5y = 46 →
  30. 30.x + 2y = −2 and 6x − 4y = −28 →
  31. 31.3x + 6y = 39 and 6x + 3y = −3 →
  32. 32.2x + 3y = 8 and 6x − y = −16 →
  33. 33.2x − y = 1 and 2x − 2y = −8 →
  34. 34.6x + y = 4 and 4x + 3y = −2 →
  35. 35.2x − 5y = 34 and 2x + 6y = −32 →
  36. 36.3x + 5y = 6 and x + 5y = −8 →
  37. 37.6x + y = 41 and 5x + 2y = 26 →
  38. 38.9x + y = 43 and x + 9y = −13 →
  39. 39.5x + y = −18 and x + 5y = 30 →
  40. 40.4x − 2y = −38 and 6x + 5y = −49 →

Answer key

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

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