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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 363 · 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 = −10 and 3x + 2y = −5 →
  2. 2.2x + 3y = 22 and x + 2y = 12 →
  3. 3.9x + 7y = 128 and 7x + 9y = 128 →
  4. 4.2x + 3y = −9 and 5x − 5y = −60 →
  5. 5.5x + 5y = −20 and x − y = −8 →
  6. 6.3x − 6y = 6 and x + 4y = 20 →
  7. 7.2x − 6y = 72 and 5x + 2y = 27 →
  8. 8.3x + 8y = 77 and 8x + 3y = 77 →
  9. 9.2x − 4y = 52 and 3x + 2y = 6 →
  10. 10.8x + 6y = 72 and 6x + 8y = 82 →
  11. 11.6x − 4y = 28 and 2x + 5y = 22 →
  12. 12.5x + 5y = 20 and 2x + 5y = 11 →
  13. 13.4x + 5y = −27 and 6x − 5y = −53 →
  14. 14.4x + 3y = −24 and 3x + y = −23 →
  15. 15.3x − 3y = −33 and 4x + 5y = 1 →
  16. 16.2x + 6y = −38 and 6x + 2y = 30 →
  17. 17.3x + 2y = −21 and 5x + 5y = −45 →
  18. 18.2x + 6y = 44 and 6x + 2y = −12 →
  19. 19.5x − y = 8 and 3x + 2y = 10 →
  20. 20.6x + 5y = −10 and 5x + y = 17 →
  21. 21.x + 4y = 28 and 2x + 6y = 46 →
  22. 22.x + 4y = −18 and 2x + 4y = −16 →
  23. 23.5x + 6y = 7 and x + 4y = 7 →
  24. 24.7x + 8y = −65 and 8x + 7y = −55 →
  25. 25.4x + 7y = −35 and 7x + 4y = 13 →
  26. 26.5x − 6y = 28 and 6x − 6y = 36 →
  27. 27.x + 5y = 46 and 6x − 4y = 4 →
  28. 28.4x − 5y = 6 and 3x − 4y = 4 →
  29. 29.6x + 5y = 67 and 3x − 2y = 11 →
  30. 30.2x + y = 9 and x + 2y = 6 →
  31. 31.5x + y = 26 and x + 5y = 10 →
  32. 32.2x + 7y = 72 and 7x + 2y = 72 →
  33. 33.2x − 4y = 6 and 3x − y = 14 →
  34. 34.4x − 6y = 6 and 4x − 5y = 7 →
  35. 35.x + 3y = 7 and 2x + 4y = 10 →
  36. 36.6x + 5y = 41 and 5x + 6y = 36 →
  37. 37.7x + 6y = 93 and 6x + 7y = 89 →
  38. 38.6x + 4y = 52 and 5x + 5y = 55 →
  39. 39.5x + 9y = 40 and 9x + 5y = 16 →
  40. 40.5x − 4y = 17 and x + 4y = 13 →

Answer key

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

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