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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 238 · 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. 1.4x − 4y = −12 and 6x + 2y = 46 →
  2. 2.4x + 6y = 38 and 2x + 6y = 28 →
  3. 3.5x + 7y = 33 and 7x + 5y = 3 →
  4. 4.2x + y = −8 and x + 2y = −1 →
  5. 5.5x + 6y = 42 and 6x + 5y = 46 →
  6. 6.3x − 5y = −42 and x + 4y = 20 →
  7. 7.2x − y = 0 and 5x + y = 21 →
  8. 8.2x − 2y = −8 and 6x + y = 18 →
  9. 9.3x + 6y = 3 and 6x + 3y = 15 →
  10. 10.5x + 2y = 31 and 6x + 2y = 40 →
  11. 11.2x + 6y = 4 and 2x + 5y = 3 →
  12. 12.x − 2y = −20 and 5x + 5y = 35 →
  13. 13.x − 6y = 49 and x + 2y = −15 →
  14. 14.2x + 8y = 46 and 8x + 2y = 4 →
  15. 15.3x + 6y = 54 and 6x + 3y = 36 →
  16. 16.x + 4y = −19 and 5x + y = 0 →
  17. 17.4x + 3y = −20 and 5x + 5y = −20 →
  18. 18.2x + 3y = 28 and 3x + 2y = 32 →
  19. 19.3x + 7y = −41 and 7x + 3y = −69 →
  20. 20.3x + 7y = −40 and 7x + 3y = −40 →
  21. 21.3x + 8y = −18 and 8x + 3y = 7 →
  22. 22.x − 6y = −57 and 5x + 3y = 12 →
  23. 23.2x + 5y = −24 and 6x − 6y = 12 →
  24. 24.9x + 6y = −69 and 6x + 9y = −66 →
  25. 25.5x + 5y = 0 and 2x − 5y = −49 →
  26. 26.2x + y = 13 and 3x + 3y = 30 →
  27. 27.x − 6y = −37 and 4x + 3y = 14 →
  28. 28.9x + 2y = 93 and 2x + 9y = 72 →
  29. 29.2x + 6y = −4 and 5x + 3y = 2 →
  30. 30.x − 2y = −14 and 6x + 5y = 52 →
  31. 31.4x + 5y = 1 and 4x + 6y = 6 →
  32. 32.4x + 3y = 25 and 2x + 3y = 17 →
  33. 33.8x + 2y = −36 and 2x + 8y = −54 →
  34. 34.4x − 2y = 18 and 4x + y = 21 →
  35. 35.6x + 2y = 28 and x + 6y = −1 →
  36. 36.2x − 2y = −28 and x + 4y = 11 →
  37. 37.3x + 2y = 0 and 4x − 3y = 17 →
  38. 38.2x + y = −17 and 5x + 2y = −41 →
  39. 39.2x + 5y = 3 and 2x + y = 7 →
  40. 40.3x + 2y = −3 and 6x + y = 3 →

Answer key

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

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