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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 491 · 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 + 4y = 22 and 4x + 6y = 28 →
  2. 2.4x + y = 24 and 5x − 3y = 13 →
  3. 3.3x − y = −18 and 2x − 5y = −38 →
  4. 4.x − 2y = −19 and x + 5y = 16 →
  5. 5.3x − y = −16 and 3x + 6y = −30 →
  6. 6.x − 5y = 52 and x − y = 16 →
  7. 7.5x + 8y = 20 and 8x + 5y = −7 →
  8. 8.7x + 5y = 54 and 5x + 7y = 66 →
  9. 9.2x + 6y = 58 and 5x − 6y = −44 →
  10. 10.x − 3y = −22 and 4x + 5y = 14 →
  11. 11.4x + y = −4 and 6x + 4y = −26 →
  12. 12.9x + y = −58 and x + 9y = 38 →
  13. 13.5x + 8y = 60 and 8x + 5y = 57 →
  14. 14.2x − 6y = −8 and 3x + y = 28 →
  15. 15.7x + 2y = 60 and 2x + 7y = 75 →
  16. 16.x + 4y = −1 and 2x + y = −9 →
  17. 17.x − 4y = 15 and 3x + 2y = 17 →
  18. 18.x + 7y = 12 and 7x + y = −12 →
  19. 19.3x + 5y = 16 and 3x − 4y = −2 →
  20. 20.3x + 2y = 12 and 2x + 3y = 13 →
  21. 21.8x + 9y = 0 and 9x + 8y = 17 →
  22. 22.5x + y = 8 and 6x + 6y = 0 →
  23. 23.5x + y = 13 and 2x + y = 10 →
  24. 24.x − 3y = −5 and x + 4y = −12 →
  25. 25.x + 4y = 20 and 4x + y = −25 →
  26. 26.4x + 2y = −24 and 3x − 5y = 34 →
  27. 27.8x + 7y = 100 and 7x + 8y = 95 →
  28. 28.2x + 3y = 29 and 4x + y = 23 →
  29. 29.x + 4y = 15 and 3x + 2y = −15 →
  30. 30.x + 4y = 38 and x − y = −2 →
  31. 31.3x − 4y = 19 and 6x + 6y = 24 →
  32. 32.3x − 5y = −32 and x + y = −8 →
  33. 33.2x + 6y = −18 and 6x + 2y = −22 →
  34. 34.3x + 4y = 3 and 4x + 3y = 18 →
  35. 35.3x − 2y = 27 and 4x + 2y = 8 →
  36. 36.2x + y = 0 and 2x − 4y = −30 →
  37. 37.9x + 7y = −91 and 7x + 9y = −85 →
  38. 38.6x − 5y = 14 and 5x + 6y = 93 →
  39. 39.3x + 5y = −1 and x + 3y = 1 →
  40. 40.4x − 6y = −22 and 4x + y = 13 →

Answer key

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

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