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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 384 · 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 + 2y = 40 and 6x + 6y = 36 →
  2. 2.2x + 3y = 37 and 3x + 2y = 38 →
  3. 3.2x + 4y = 38 and 4x + 2y = 46 →
  4. 4.3x − 2y = 15 and 4x − y = 10 →
  5. 5.4x − 2y = 26 and 2x − 6y = 58 →
  6. 6.9x + 8y = 20 and 8x + 9y = 31 →
  7. 7.x − 3y = −23 and 2x + 3y = −1 →
  8. 8.4x − 3y = 17 and 3x + 6y = 21 →
  9. 9.4x + 3y = −32 and 3x + 4y = −38 →
  10. 10.6x − 4y = 26 and 2x + y = 25 →
  11. 11.4x + 5y = −11 and 5x + 4y = −25 →
  12. 12.6x + 6y = −72 and 4x − y = −28 →
  13. 13.4x − 6y = 50 and x + y = 5 →
  14. 14.4x + 5y = 1 and 5x + 4y = 8 →
  15. 15.x + 4y = 15 and 3x + 5y = 31 →
  16. 16.5x + 6y = 39 and x − 5y = −17 →
  17. 17.x + 2y = −9 and 4x − 6y = 6 →
  18. 18.5x − 4y = 13 and 2x + 5y = 25 →
  19. 19.5x − 6y = −1 and 6x + 5y = 72 →
  20. 20.6x + 2y = 2 and x + 2y = −3 →
  21. 21.2x + y = 22 and 5x − 4y = 29 →
  22. 22.2x + 5y = −1 and 5x + 2y = −34 →
  23. 23.6x + 7y = 53 and 7x + 6y = 51 →
  24. 24.7x + 2y = 11 and 2x + 7y = 16 →
  25. 25.3x − 2y = −20 and 3x + 4y = −14 →
  26. 26.4x + y = 13 and x + 4y = 37 →
  27. 27.6x + y = 3 and x + 6y = −52 →
  28. 28.3x + 4y = −8 and 4x + 3y = 1 →
  29. 29.3x + 4y = −2 and 5x + 3y = 15 →
  30. 30.2x − 5y = −3 and 3x − 6y = −3 →
  31. 31.3x + 2y = 17 and 2x + 3y = 8 →
  32. 32.7x + 6y = −110 and 6x + 7y = −111 →
  33. 33.2x − 5y = 1 and 5x − 2y = −29 →
  34. 34.2x + 2y = −4 and x − 3y = −18 →
  35. 35.5x + 2y = 53 and x + 4y = 43 →
  36. 36.5x + y = 11 and x + 5y = 7 →
  37. 37.7x + 8y = 29 and 8x + 7y = 31 →
  38. 38.4x + 7y = 1 and 7x + 4y = 43 →
  39. 39.2x + y = 15 and x + 2y = 15 →
  40. 40.x + 2y = −1 and 2x + y = 1 →

Answer key

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

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