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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 31 · 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 + 6y = −28 and 4x + 2y = −16 →
  2. 2.5x + y = −36 and x + y = −8 →
  3. 3.7x + y = 52 and x + 7y = 28 →
  4. 4.4x + 5y = 28 and 3x + 2y = 14 →
  5. 5.x + 4y = 31 and 3x + 2y = 33 →
  6. 6.3x + 5y = 8 and 5x + 3y = 8 →
  7. 7.3x + 4y = 25 and 4x + 3y = 31 →
  8. 8.x − y = −15 and 4x + 5y = 12 →
  9. 9.5x + 8y = 77 and 8x + 5y = 53 →
  10. 10.3x + 9y = 45 and 9x + 3y = 63 →
  11. 11.x + 6y = 47 and 6x + y = 37 →
  12. 12.8x + 3y = −81 and 3x + 8y = −51 →
  13. 13.5x + 6y = −23 and x + 3y = −10 →
  14. 14.2x − 4y = −22 and x + 6y = 37 →
  15. 15.5x + 6y = 39 and 6x − 5y = −2 →
  16. 16.2x + 4y = 24 and 6x + 5y = 37 →
  17. 17.x + 3y = −8 and 2x + 5y = −15 →
  18. 18.x + 4y = 13 and x + 6y = 17 →
  19. 19.4x + 4y = −28 and 2x + 4y = −30 →
  20. 20.3x − y = 22 and 4x + 6y = 22 →
  21. 21.5x + y = 0 and 6x + 6y = 24 →
  22. 22.5x + 3y = 29 and x + 2y = 17 →
  23. 23.3x + y = 22 and 2x + y = 17 →
  24. 24.6x + y = 28 and 2x − y = 12 →
  25. 25.x − 4y = −34 and 4x − 5y = −37 →
  26. 26.5x + 2y = 52 and 2x + 5y = 46 →
  27. 27.4x + 2y = −20 and 2x + 4y = 2 →
  28. 28.5x + 4y = 27 and 5x + 6y = 43 →
  29. 29.3x − 3y = 0 and 2x + y = −6 →
  30. 30.4x + 8y = 28 and 8x + 4y = 44 →
  31. 31.x + 9y = 10 and 9x + y = 10 →
  32. 32.x + 6y = 12 and 6x − 3y = 33 →
  33. 33.5x + 6y = 71 and 2x − 3y = −4 →
  34. 34.x + 2y = 13 and 4x + 6y = 46 →
  35. 35.2x + y = 7 and x + 2y = 17 →
  36. 36.2x + 6y = −22 and 2x − 5y = 11 →
  37. 37.3x − 3y = −12 and 4x + y = −1 →
  38. 38.2x + 7y = 21 and 7x + 2y = −39 →
  39. 39.x + 4y = 25 and x + 5y = 31 →
  40. 40.x + 5y = 37 and 5x + y = 41 →

Answer key

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

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