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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 206 · 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. 1.3x + 4y = 3 and 3x + 6y = 9 →
  2. 2.3x − 6y = −21 and 4x + 5y = −15 →
  3. 3.4x + 5y = −71 and 3x − 3y = −6 →
  4. 4.2x + 2y = 18 and 4x − y = 16 →
  5. 5.5x + 5y = 30 and x − 6y = −29 →
  6. 6.2x − y = 10 and 3x + 5y = −37 →
  7. 7.9x + 3y = 66 and 3x + 9y = 6 →
  8. 8.6x + 8y = 60 and 8x + 6y = 66 →
  9. 9.5x − 2y = 17 and x − 3y = −7 →
  10. 10.6x + y = 16 and x + 6y = −9 →
  11. 11.6x + y = 46 and 6x − 3y = 30 →
  12. 12.7x + 4y = 39 and 4x + 7y = 60 →
  13. 13.9x + 4y = 45 and 4x + 9y = −45 →
  14. 14.4x + 2y = 22 and x − y = −8 →
  15. 15.3x + 2y = 1 and 2x + 3y = −6 →
  16. 16.2x + 8y = −58 and 8x + 2y = −22 →
  17. 17.2x + 3y = 15 and 6x + 3y = −9 →
  18. 18.x − y = −15 and 2x + 2y = −6 →
  19. 19.6x + 5y = 9 and x + 4y = −27 →
  20. 20.2x + 8y = 66 and 8x + 2y = 24 →
  21. 21.4x + y = 2 and 4x + 4y = −16 →
  22. 22.3x + y = −18 and x − y = −2 →
  23. 23.x − y = −1 and 3x + 6y = 69 →
  24. 24.2x + 9y = 67 and 9x + 2y = 32 →
  25. 25.x + 6y = 55 and 4x + 6y = 76 →
  26. 26.2x + y = −9 and x + 2y = 9 →
  27. 27.4x + 6y = 16 and 6x + 4y = −16 →
  28. 28.4x + 4y = 8 and 4x + 6y = 26 →
  29. 29.6x + y = 29 and 3x + y = 11 →
  30. 30.x − 3y = 22 and 3x − 6y = 48 →
  31. 31.4x + 5y = −27 and 4x − 3y = −35 →
  32. 32.3x + 6y = 36 and 2x − 2y = 6 →
  33. 33.3x + 6y = 27 and 2x + 5y = 21 →
  34. 34.5x − y = 38 and 3x − 2y = 13 →
  35. 35.8x + 2y = 24 and 2x + 8y = 36 →
  36. 36.x + 6y = 39 and 6x + y = 59 →
  37. 37.3x + 6y = −36 and 6x − 2y = −16 →
  38. 38.2x + 5y = −23 and 3x + 6y = −27 →
  39. 39.3x − 2y = 21 and 4x − 3y = 31 →
  40. 40.6x − 4y = −6 and 3x + y = 15 →

Answer key

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

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