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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 606 · 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 + 4y = 42 and 4x + 2y = 30 →
  2. 2.x + 3y = 16 and 4x + 2y = 14 →
  3. 3.x + 5y = −14 and 6x − y = 40 →
  4. 4.x + 8y = 63 and 8x + y = −63 →
  5. 5.9x + 8y = 17 and 8x + 9y = 17 →
  6. 6.5x − 5y = −30 and 5x + 2y = 19 →
  7. 7.7x + y = 38 and x + 7y = 26 →
  8. 8.5x + 6y = 22 and 3x + 3y = 12 →
  9. 9.4x + 7y = 36 and 7x + 4y = 30 →
  10. 10.x + 2y = −7 and 2x + y = 10 →
  11. 11.3x − 5y = −8 and x − 5y = −16 →
  12. 12.3x + 2y = −9 and 2x + 3y = 9 →
  13. 13.5x + y = 26 and x + 4y = 28 →
  14. 14.6x − 3y = −42 and x + 5y = 15 →
  15. 15.6x − 2y = 52 and 3x + 2y = 11 →
  16. 16.x + 6y = 16 and 5x + 6y = −16 →
  17. 17.3x + 2y = −9 and 5x + 3y = −13 →
  18. 18.2x − 4y = 24 and 2x − 3y = 21 →
  19. 19.4x − 3y = 6 and 2x − 6y = −6 →
  20. 20.4x − 5y = −6 and 5x + 3y = 11 →
  21. 21.3x + 2y = 16 and 4x + y = 23 →
  22. 22.5x + 3y = −9 and 4x − 2y = 28 →
  23. 23.x − 2y = 25 and 2x + y = 5 →
  24. 24.2x + 2y = 24 and x + 3y = 18 →
  25. 25.9x + 5y = 87 and 5x + 9y = 67 →
  26. 26.4x − 4y = −40 and 5x + 2y = −8 →
  27. 27.2x + 5y = 6 and 3x − 2y = −29 →
  28. 28.5x + 4y = 18 and 3x − 5y = −41 →
  29. 29.3x + 9y = 45 and 9x + 3y = 87 →
  30. 30.3x + 6y = 57 and 4x − 5y = −15 →
  31. 31.x + 6y = 10 and 4x − 5y = −47 →
  32. 32.3x − 2y = −22 and 6x + 5y = 1 →
  33. 33.2x + y = 23 and x + 2y = 25 →
  34. 34.x − 2y = 10 and x + y = 4 →
  35. 35.6x + 6y = 36 and x + 5y = 10 →
  36. 36.4x − 5y = −24 and 5x + 4y = 11 →
  37. 37.4x + y = 31 and x + 4y = 4 →
  38. 38.x + y = 10 and 6x + 3y = 42 →
  39. 39.2x + 3y = 19 and 3x − 6y = −24 →
  40. 40.4x − 3y = −5 and 2x + 2y = −20 →

Answer key

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

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