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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 805 · 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 = −8 and 3x − 3y = 0 →
  2. 2.2x + 4y = 18 and 4x + 2y = 0 →
  3. 3.7x + y = −58 and x + 7y = −22 →
  4. 4.6x + y = −21 and x + 6y = 14 →
  5. 5.x − 5y = 19 and x − y = 7 →
  6. 6.x − 2y = 15 and 3x − 3y = 30 →
  7. 7.9x + 6y = −6 and 6x + 9y = 6 →
  8. 8.3x + 5y = 13 and 4x + 4y = 20 →
  9. 9.6x + y = −15 and x + y = −5 →
  10. 10.4x + 3y = 5 and 3x + 4y = −12 →
  11. 11.3x − 4y = −1 and 2x − 6y = −24 →
  12. 12.2x + 5y = −21 and 4x − y = 13 →
  13. 13.6x − 5y = −14 and 5x + 3y = 17 →
  14. 14.x + 4y = 22 and 2x + 6y = 36 →
  15. 15.5x − 5y = 15 and 3x + 4y = 51 →
  16. 16.5x + y = 45 and x + 5y = 33 →
  17. 17.3x + 3y = 24 and 5x + 3y = 28 →
  18. 18.4x − y = 16 and x − 5y = 23 →
  19. 19.5x + 4y = 26 and 4x + 5y = 28 →
  20. 20.x + 8y = 54 and 8x + y = 54 →
  21. 21.x − 4y = −22 and 4x − 2y = −4 →
  22. 22.4x + y = 2 and 6x + 2y = 6 →
  23. 23.2x + 2y = 14 and 5x + y = 31 →
  24. 24.3x − 4y = 42 and 2x + 3y = −6 →
  25. 25.x + 5y = −36 and 5x + y = 36 →
  26. 26.x + 2y = −11 and 2x + y = −4 →
  27. 27.4x − y = 33 and 3x − 3y = 18 →
  28. 28.4x + 6y = −30 and 6x + 4y = 0 →
  29. 29.6x − 5y = 76 and 6x − 3y = 60 →
  30. 30.2x + 9y = 65 and 9x + 2y = 23 →
  31. 31.4x + 5y = −11 and 5x + 4y = −16 →
  32. 32.4x + 9y = 54 and 9x + 4y = 89 →
  33. 33.x + 2y = 4 and 2x + y = −7 →
  34. 34.x + 5y = −43 and 5x + y = −23 →
  35. 35.6x + 4y = 6 and 4x + 6y = 24 →
  36. 36.x + 7y = 45 and 7x + y = −21 →
  37. 37.x − 3y = 25 and 4x + 6y = −44 →
  38. 38.5x + 3y = 51 and 5x + y = 37 →
  39. 39.3x + 3y = 0 and 2x + 3y = 1 →
  40. 40.5x − 6y = −34 and 5x + 2y = −42 →

Answer key

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

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