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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 538 · 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. 1.2x + 3y = 35 and 5x + 3y = 56 →
  2. 2.5x + 4y = 28 and 4x + 5y = 17 →
  3. 3.x + 2y = 17 and x + 5y = 35 →
  4. 4.x + 4y = −21 and 4x + y = 21 →
  5. 5.x + 6y = 39 and 4x − 6y = −54 →
  6. 6.9x + 5y = −53 and 5x + 9y = −17 →
  7. 7.x + 5y = 48 and 4x + 2y = 30 →
  8. 8.5x + 6y = 21 and 3x + 3y = 12 →
  9. 9.2x + 4y = 24 and 5x + 4y = 42 →
  10. 10.3x + 4y = 19 and 3x + 6y = 21 →
  11. 11.4x + 4y = −56 and 2x + 6y = −56 →
  12. 12.4x + 8y = −48 and 8x + 4y = −72 →
  13. 13.x + 2y = 5 and 6x + 5y = 16 →
  14. 14.8x + 3y = 78 and 3x + 8y = 43 →
  15. 15.6x + 2y = −36 and x + 3y = 10 →
  16. 16.7x + 3y = 87 and 3x + 7y = 83 →
  17. 17.6x + 5y = 53 and 5x + 6y = 46 →
  18. 18.6x + 4y = −14 and 4x + 6y = 14 →
  19. 19.2x + y = 26 and x + 3y = 33 →
  20. 20.7x + 9y = −4 and 9x + 7y = −28 →
  21. 21.4x + 2y = 32 and 2x + 2y = 24 →
  22. 22.9x + 3y = −57 and 3x + 9y = −3 →
  23. 23.2x + 9y = 57 and 9x + 2y = −13 →
  24. 24.2x + 3y = 11 and 3x + 2y = −6 →
  25. 25.4x + y = 19 and x + 4y = −14 →
  26. 26.x − 3y = −15 and 6x − 5y = 1 →
  27. 27.5x + 2y = 7 and 4x + 6y = −12 →
  28. 28.4x + y = −20 and 2x + 4y = 18 →
  29. 29.2x + 5y = −1 and 5x + 2y = 29 →
  30. 30.6x + 4y = 72 and 4x − y = 26 →
  31. 31.x + 2y = 15 and x + 6y = 39 →
  32. 32.x − 4y = −12 and 4x + 5y = −27 →
  33. 33.x + 4y = 22 and 3x − 4y = 2 →
  34. 34.x + y = −3 and 5x + 6y = −17 →
  35. 35.5x + 6y = 58 and 3x + y = 14 →
  36. 36.2x − 6y = −48 and 4x − 6y = −42 →
  37. 37.6x − y = 28 and 3x + 2y = 34 →
  38. 38.7x + 8y = 4 and 8x + 7y = −4 →
  39. 39.4x + y = 13 and x + 4y = 22 →
  40. 40.3x + 6y = 48 and 6x + 3y = 60 →

Answer key

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

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