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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 782 · 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 + 3y = −49 and 3x + 8y = 16 →
  2. 2.6x + 4y = 62 and x − y = 2 →
  3. 3.6x − 5y = 1 and 3x + 2y = 32 →
  4. 4.5x + 2y = 3 and x + 2y = −1 →
  5. 5.3x − 5y = −22 and 5x + 2y = 46 →
  6. 6.7x + 5y = −16 and 5x + 7y = −32 →
  7. 7.8x + 3y = −42 and 3x + 8y = −57 →
  8. 8.4x + 5y = −15 and 5x + 4y = −3 →
  9. 9.x − 2y = −13 and 2x + y = 4 →
  10. 10.2x + y = 10 and 5x − y = 32 →
  11. 11.x + 2y = 9 and 4x − 3y = −30 →
  12. 12.3x + 6y = 69 and x + 6y = 55 →
  13. 13.2x + 5y = 55 and 3x + 2y = 33 →
  14. 14.4x + y = 5 and 6x − y = 15 →
  15. 15.2x − 2y = 0 and x + 3y = 4 →
  16. 16.2x + 5y = −7 and 2x + 4y = −4 →
  17. 17.2x + y = −4 and 6x + 2y = −4 →
  18. 18.2x + 4y = 46 and 4x + 2y = 38 →
  19. 19.2x + 7y = −40 and 7x + 2y = −50 →
  20. 20.4x − 4y = 0 and 6x + 5y = 55 →
  21. 21.x + 4y = 8 and 4x + y = 17 →
  22. 22.2x + 2y = 24 and 5x − 6y = −6 →
  23. 23.4x + 8y = −20 and 8x + 4y = 8 →
  24. 24.5x − y = −22 and 5x + 6y = −8 →
  25. 25.6x − y = 36 and 2x + y = 4 →
  26. 26.4x + 9y = 20 and 9x + 4y = −20 →
  27. 27.3x + 2y = 25 and 2x + 3y = 15 →
  28. 28.6x + 6y = 30 and 6x + 2y = 18 →
  29. 29.9x + 2y = 17 and 2x + 9y = −39 →
  30. 30.2x + 6y = 62 and 3x + 6y = 69 →
  31. 31.9x + 2y = 14 and 2x + 9y = −14 →
  32. 32.4x + 2y = −20 and 2x + 4y = −4 →
  33. 33.x − 6y = −43 and 5x − 2y = −47 →
  34. 34.6x − 3y = 39 and x + 5y = −21 →
  35. 35.9x + 8y = 66 and 8x + 9y = 70 →
  36. 36.5x + 2y = −28 and 2x + 5y = 14 →
  37. 37.x − 3y = −13 and 3x + 6y = 21 →
  38. 38.3x + 8y = −43 and 8x + 3y = −23 →
  39. 39.9x + 6y = 51 and 6x + 9y = 54 →
  40. 40.7x + 2y = −58 and 2x + 7y = −23 →

Answer key

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

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