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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 49 · 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. 1.8x + 9y = −11 and 9x + 8y = −6 →
  2. 2.5x + 2y = 12 and 6x − 3y = 36 →
  3. 3.6x + 4y = 8 and 4x + 6y = 2 →
  4. 4.3x − 3y = −45 and 4x − y = −39 →
  5. 5.4x + 6y = 10 and 6x + 4y = −20 →
  6. 6.2x + 4y = 52 and 3x − 4y = −12 →
  7. 7.5x − 3y = 14 and 2x + 4y = 16 →
  8. 8.2x + 6y = 28 and x − 3y = 2 →
  9. 9.9x + 4y = 53 and 4x + 9y = 38 →
  10. 10.2x + 5y = 7 and 5x + 2y = 7 →
  11. 11.6x + 5y = −49 and 5x + 6y = −39 →
  12. 12.x + 2y = 15 and 5x − 6y = 11 →
  13. 13.7x + 4y = 27 and 4x + 7y = 6 →
  14. 14.x + 6y = 39 and x − 6y = −45 →
  15. 15.2x − 2y = −22 and 6x + 2y = −2 →
  16. 16.5x + 3y = 7 and 5x − 3y = 13 →
  17. 17.3x + 9y = 48 and 9x + 3y = −24 →
  18. 18.4x + y = −6 and 2x − y = −12 →
  19. 19.4x + 3y = −1 and 3x + 4y = 8 →
  20. 20.2x + 5y = −22 and x + 6y = −32 →
  21. 21.2x + 6y = 14 and 4x − 2y = 0 →
  22. 22.x + y = 12 and 5x + 6y = 67 →
  23. 23.6x + 3y = 18 and 3x + 6y = 27 →
  24. 24.6x + y = −21 and 3x + y = −9 →
  25. 25.2x + 3y = 12 and 4x − 3y = 6 →
  26. 26.5x + y = 4 and x + 5y = 44 →
  27. 27.x + 5y = 48 and 5x + 4y = 51 →
  28. 28.2x + 6y = 26 and 6x + 2y = −34 →
  29. 29.3x + 9y = −84 and 9x + 3y = −60 →
  30. 30.x + 3y = −5 and 5x + 3y = 11 →
  31. 31.6x + 4y = 14 and 2x + 3y = 13 →
  32. 32.6x + 4y = −58 and 4x + 6y = −62 →
  33. 33.5x − y = 11 and x − y = 7 →
  34. 34.3x + 7y = 47 and 7x + 3y = 43 →
  35. 35.x + 4y = 9 and 5x − 4y = 21 →
  36. 36.4x + 6y = 32 and 5x + y = 27 →
  37. 37.2x + 2y = 12 and 6x − y = −27 →
  38. 38.x + 2y = −1 and 2x − 2y = 22 →
  39. 39.2x + y = 22 and x + 2y = 20 →
  40. 40.8x + 5y = 109 and 5x + 8y = 112 →

Answer key

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

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