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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 113 · 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 + 4y = −18 and 2x + 3y = −15 →
  2. 2.4x + 5y = −6 and 2x + y = 6 →
  3. 3.2x + 9y = 7 and 9x + 2y = 70 →
  4. 4.2x + 2y = −6 and 6x − 4y = 32 →
  5. 5.6x + 2y = −6 and 2x + 6y = 30 →
  6. 6.7x + 6y = −12 and 6x + 7y = −1 →
  7. 7.9x + 4y = 12 and 4x + 9y = −38 →
  8. 8.3x + 4y = 22 and 5x + y = 14 →
  9. 9.4x + 2y = 16 and 3x − 5y = 25 →
  10. 10.3x + 2y = −33 and 2x + 3y = −27 →
  11. 11.4x + 2y = 30 and 2x + 4y = 18 →
  12. 12.9x + y = −43 and x + 9y = 13 →
  13. 13.5x + 5y = −5 and x − 3y = 27 →
  14. 14.2x + 3y = 2 and x + 6y = 19 →
  15. 15.2x − 3y = 45 and x + 2y = −9 →
  16. 16.4x + 6y = −42 and 6x + 4y = −48 →
  17. 17.2x + 6y = −26 and 3x + y = −7 →
  18. 18.2x + y = 16 and 6x + 6y = 54 →
  19. 19.5x + 5y = 65 and 2x + y = 19 →
  20. 20.x + 2y = 4 and x − 3y = 9 →
  21. 21.x + 3y = −15 and 2x + y = −15 →
  22. 22.7x + 8y = 100 and 8x + 7y = 95 →
  23. 23.2x + 5y = 29 and 5x + 2y = 41 →
  24. 24.x − 2y = −2 and 6x + 6y = 24 →
  25. 25.2x + 5y = 37 and x + 3y = 22 →
  26. 26.2x − y = −1 and 4x + 3y = 33 →
  27. 27.2x − 6y = −36 and 2x − 3y = −12 →
  28. 28.2x + 9y = 24 and 9x + 2y = 31 →
  29. 29.3x + 6y = 21 and 2x + y = 5 →
  30. 30.4x + y = 20 and x + 4y = 20 →
  31. 31.x − 5y = −13 and x + y = 5 →
  32. 32.3x + 6y = −18 and x − 2y = 10 →
  33. 33.6x + 3y = 21 and 6x − 2y = 6 →
  34. 34.2x + y = 19 and 2x − 3y = −1 →
  35. 35.4x − 2y = 12 and 3x + 6y = 54 →
  36. 36.5x + 2y = 28 and x − 5y = −16 →
  37. 37.4x + 2y = −4 and 5x + y = 7 →
  38. 38.x + 3y = −12 and 4x + y = 7 →
  39. 39.9x + 5y = 66 and 5x + 9y = 74 →
  40. 40.5x + 7y = −3 and 7x + 5y = −9 →

Answer key

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

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