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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 963 · 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 + 3y = 42 and 4x + 2y = 40 →
  2. 2.6x − 3y = 51 and 3x + 6y = −27 →
  3. 3.4x − 3y = 14 and x − 6y = −28 →
  4. 4.6x − y = −3 and 2x + 2y = −22 →
  5. 5.4x − 2y = 4 and 6x + 2y = 16 →
  6. 6.5x + 5y = −65 and 4x − 2y = 2 →
  7. 7.2x − y = −25 and 5x + 5y = 5 →
  8. 8.2x − 6y = −4 and 4x − 6y = 10 →
  9. 9.4x + 3y = 10 and 5x − 3y = −1 →
  10. 10.2x + 4y = 6 and 4x + 2y = 30 →
  11. 11.x − 6y = −9 and x + 6y = 27 →
  12. 12.3x + 2y = 10 and 2x + 3y = 10 →
  13. 13.7x + y = 27 and x + 7y = 45 →
  14. 14.3x − 2y = 2 and 2x − 3y = −7 →
  15. 15.3x + y = 20 and x + 3y = 20 →
  16. 16.2x + 5y = 17 and 6x + 6y = 24 →
  17. 17.4x + y = −45 and 6x − 3y = −27 →
  18. 18.5x + y = 36 and 3x − 6y = 15 →
  19. 19.6x + 4y = 46 and x + 5y = 12 →
  20. 20.x + 6y = −1 and 6x + y = −41 →
  21. 21.4x + 7y = 53 and 7x + 4y = 35 →
  22. 22.x + 4y = 15 and x + 2y = 9 →
  23. 23.x − 6y = −16 and x + 3y = 11 →
  24. 24.4x + 6y = 14 and x + 2y = 3 →
  25. 25.6x + 6y = −6 and x − 4y = −16 →
  26. 26.5x + 3y = 27 and 4x − 2y = 4 →
  27. 27.2x + 2y = 16 and 5x − 3y = 8 →
  28. 28.4x + 6y = −12 and 2x − 2y = 14 →
  29. 29.2x + 3y = 12 and 3x + 2y = 13 →
  30. 30.6x − y = 15 and 4x + 5y = 61 →
  31. 31.3x + 7y = 71 and 7x + 3y = 59 →
  32. 32.2x + y = 13 and 5x + 3y = 35 →
  33. 33.6x + y = −15 and x + 6y = −20 →
  34. 34.2x − 6y = 22 and 3x + 2y = −33 →
  35. 35.x + 5y = 45 and 4x + 3y = 44 →
  36. 36.3x + 6y = −27 and 6x + 3y = −9 →
  37. 37.3x + 2y = 19 and 2x + 3y = 21 →
  38. 38.x + 2y = −2 and 4x + 3y = 2 →
  39. 39.4x + 8y = −44 and 8x + 4y = −16 →
  40. 40.x + 6y = −19 and 6x − 5y = 9 →

Answer key

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

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