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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 659 · 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. 1.3x − 3y = 24 and 5x + y = −14 →
  2. 2.6x + 5y = 49 and 2x + 3y = 15 →
  3. 3.3x + y = −2 and 6x + 6y = −36 →
  4. 4.x + y = 8 and 3x + y = 20 →
  5. 5.3x + y = 19 and x + 3y = 17 →
  6. 6.x + 8y = 58 and 8x + y = −40 →
  7. 7.4x − 4y = 0 and 2x + y = −15 →
  8. 8.4x + y = −4 and 5x + 4y = −27 →
  9. 9.2x − y = −8 and 6x + 4y = −80 →
  10. 10.4x − 2y = 50 and 3x − 2y = 42 →
  11. 11.x + 5y = 13 and 4x + 3y = 18 →
  12. 12.8x + 4y = −16 and 4x + 8y = 28 →
  13. 13.6x + 3y = 39 and 5x + y = 28 →
  14. 14.4x − 5y = −32 and x − 5y = −38 →
  15. 15.3x + 5y = 32 and 3x + 6y = 33 →
  16. 16.x + 2y = 23 and 2x + y = 25 →
  17. 17.3x + y = −5 and 4x + 3y = −5 →
  18. 18.x + 6y = 45 and 4x + 2y = −18 →
  19. 19.5x + 2y = 17 and 3x − 2y = −9 →
  20. 20.4x + y = 31 and 2x + 6y = 32 →
  21. 21.3x + 9y = −15 and 9x + 3y = 3 →
  22. 22.2x − 2y = −8 and 2x + 6y = 56 →
  23. 23.3x + 3y = −6 and x − 2y = −17 →
  24. 24.x + 6y = 15 and 2x + 3y = 12 →
  25. 25.6x + 5y = 50 and 2x − y = 6 →
  26. 26.5x − 4y = −2 and 2x + y = 7 →
  27. 27.x + y = −6 and 3x + 5y = −32 →
  28. 28.x + 4y = 22 and 4x + y = 28 →
  29. 29.3x + 2y = 26 and 5x − 4y = 36 →
  30. 30.9x + 3y = −57 and 3x + 9y = −51 →
  31. 31.x + 2y = −11 and 5x − 2y = 29 →
  32. 32.x − 2y = −1 and x + 4y = 5 →
  33. 33.x + 6y = 11 and 6x − 6y = −18 →
  34. 34.3x − 3y = 33 and 2x + y = −5 →
  35. 35.5x + 3y = 7 and 5x + 4y = 6 →
  36. 36.4x + 7y = 46 and 7x + 4y = 31 →
  37. 37.6x + 5y = −20 and 3x − 4y = −23 →
  38. 38.4x − 2y = −16 and 2x + 3y = 8 →
  39. 39.x − 4y = −3 and 2x + 3y = 27 →
  40. 40.5x + 5y = 25 and x + 5y = 13 →

Answer key

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

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