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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 436 · 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 + 2y = −26 and 2x + 3y = −29 →
  2. 2.6x − 6y = −78 and 3x − 5y = −51 →
  3. 3.3x + 6y = −57 and 2x + y = −17 →
  4. 4.7x + 3y = −25 and 3x + 7y = −5 →
  5. 5.6x − y = −7 and 6x − 4y = −10 →
  6. 6.2x + 6y = 36 and 6x + 2y = −36 →
  7. 7.5x + y = 1 and x + 5y = 29 →
  8. 8.3x + 4y = 1 and 2x + 2y = 2 →
  9. 9.5x + 5y = 30 and x + 4y = 27 →
  10. 10.4x + 2y = −28 and 2x + 4y = −2 →
  11. 11.6x + 3y = 51 and 2x + 6y = 42 →
  12. 12.x + 5y = 49 and 5x + y = 53 →
  13. 13.3x + y = 8 and x − y = 4 →
  14. 14.x + 3y = 21 and 3x + y = 15 →
  15. 15.x + 4y = 17 and 2x − 2y = −6 →
  16. 16.5x − 6y = −32 and 3x + 6y = 48 →
  17. 17.8x + 2y = 68 and 2x + 8y = 32 →
  18. 18.x + 8y = 54 and 8x + y = 54 →
  19. 19.6x + 2y = 56 and 6x + 5y = 68 →
  20. 20.7x + y = 37 and x + 7y = −29 →
  21. 21.x + 3y = 29 and 3x + y = 15 →
  22. 22.x + 9y = −45 and 9x + y = 75 →
  23. 23.x + 4y = −27 and 5x + 4y = 9 →
  24. 24.3x + 9y = 57 and 9x + 3y = −21 →
  25. 25.3x + 5y = 8 and x + 3y = 4 →
  26. 26.4x + 5y = 46 and x + 5y = 19 →
  27. 27.8x + 7y = −27 and 7x + 8y = −18 →
  28. 28.6x + 5y = −60 and 5x + 6y = −61 →
  29. 29.2x + 5y = 39 and x − 2y = −3 →
  30. 30.5x + 2y = 9 and x − 5y = 45 →
  31. 31.x − 4y = 17 and 4x + 2y = 32 →
  32. 32.9x + 5y = 50 and 5x + 9y = 34 →
  33. 33.6x + 5y = −57 and 4x + 3y = −35 →
  34. 34.3x + 6y = −24 and 5x − 4y = 58 →
  35. 35.2x − 3y = 2 and 2x + 2y = 22 →
  36. 36.6x + 2y = 46 and 5x + y = 33 →
  37. 37.8x + 9y = −79 and 9x + 8y = −74 →
  38. 38.2x + 4y = 26 and 4x + 2y = 22 →
  39. 39.x + 4y = −25 and x + 2y = −11 →
  40. 40.7x + 3y = −5 and 3x + 7y = 15 →

Answer key

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

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