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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 341 · 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 − 6y = −39 and 5x + 6y = 47 →
  2. 2.6x + y = 21 and x + 6y = 21 →
  3. 3.x + 3y = 16 and 3x + y = 8 →
  4. 4.4x + 3y = 2 and 3x + 4y = −2 →
  5. 5.3x − 4y = −14 and x − 6y = −42 →
  6. 6.3x + 3y = 24 and 5x + 2y = 37 →
  7. 7.4x + 2y = 26 and 2x + 4y = 28 →
  8. 8.7x + 5y = 4 and 5x + 7y = −4 →
  9. 9.2x + 5y = 9 and 3x + y = −6 →
  10. 10.x + 2y = 7 and x + 5y = 19 →
  11. 11.5x − 2y = 3 and 3x + 2y = −27 →
  12. 12.x + 9y = 14 and 9x + y = 46 →
  13. 13.3x + 6y = 45 and 5x − 2y = −9 →
  14. 14.x + 9y = 19 and 9x + y = 11 →
  15. 15.x + y = −3 and 6x − 3y = 54 →
  16. 16.4x + 8y = 36 and 8x + 4y = −36 →
  17. 17.4x + 2y = 0 and 4x + y = 6 →
  18. 18.x + 4y = 8 and 6x − 5y = 19 →
  19. 19.4x + 7y = 23 and 7x + 4y = −1 →
  20. 20.2x + 7y = 66 and 7x + 2y = 51 →
  21. 21.2x + 5y = 4 and 5x + 2y = 31 →
  22. 22.3x + 4y = −8 and 4x + y = 24 →
  23. 23.x + 5y = −43 and 5x + y = 1 →
  24. 24.5x + 3y = 69 and 3x + 5y = 67 →
  25. 25.x + 4y = 6 and 5x + 2y = −6 →
  26. 26.x + 3y = −23 and 2x − 4y = 14 →
  27. 27.6x − 2y = −18 and 5x − 6y = −28 →
  28. 28.3x + y = −15 and 5x − 5y = −65 →
  29. 29.2x − y = 18 and 5x − y = 42 →
  30. 30.x + 2y = 8 and 2x + 6y = 22 →
  31. 31.3x − y = 33 and 6x + y = 39 →
  32. 32.9x + y = −66 and x + 9y = 46 →
  33. 33.3x + 6y = −6 and 6x + 3y = 6 →
  34. 34.2x + 6y = 64 and 4x + 2y = 38 →
  35. 35.7x + 8y = 104 and 8x + 7y = 106 →
  36. 36.6x + 4y = 64 and 6x − 5y = 1 →
  37. 37.x + 3y = 23 and x − 2y = −7 →
  38. 38.2x + 5y = −14 and 6x + 4y = −20 →
  39. 39.x + y = −8 and 6x + 3y = −45 →
  40. 40.5x + 3y = −22 and 5x + 2y = −23 →

Answer key

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

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