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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 961 · 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. 1.9x + y = −17 and x + 9y = 7 →
  2. 2.5x + 5y = 15 and 2x + 3y = 1 →
  3. 3.3x − 5y = 18 and 4x + 5y = −11 →
  4. 4.7x + 9y = 130 and 9x + 7y = 126 →
  5. 5.4x + y = 31 and 3x − 4y = 28 →
  6. 6.8x + 4y = −24 and 4x + 8y = 36 →
  7. 7.x + y = 5 and 4x − 2y = −28 →
  8. 8.3x + 3y = 18 and 5x + 3y = 16 →
  9. 9.4x + 6y = −28 and 5x + 5y = −25 →
  10. 10.x − 2y = −15 and 3x + 6y = −9 →
  11. 11.5x − 2y = −27 and 4x − 6y = −48 →
  12. 12.4x + 9y = 38 and 9x + 4y = 53 →
  13. 13.3x + 6y = 12 and 2x − y = −17 →
  14. 14.x + 7y = 18 and 7x + y = 30 →
  15. 15.5x − 5y = −30 and x − 5y = −22 →
  16. 16.7x + 8y = 48 and 8x + 7y = 57 →
  17. 17.x + 4y = 34 and 4x + y = 16 →
  18. 18.2x − 6y = 18 and x + 5y = −23 →
  19. 19.4x + 5y = 20 and x + 2y = 11 →
  20. 20.2x − 3y = 5 and 4x − 2y = 22 →
  21. 21.3x + 5y = 21 and x − y = −17 →
  22. 22.8x + 6y = −22 and 6x + 8y = 8 →
  23. 23.5x + 3y = −1 and 5x + 6y = 23 →
  24. 24.x + y = 2 and 2x + 6y = 8 →
  25. 25.3x + 9y = 69 and 9x + 3y = 63 →
  26. 26.5x + 2y = 53 and 2x + 5y = 59 →
  27. 27.2x + 7y = 23 and 7x + 2y = 13 →
  28. 28.5x + 9y = 57 and 9x + 5y = 13 →
  29. 29.4x + y = 16 and x + y = 7 →
  30. 30.4x + 4y = −36 and 5x + 2y = −24 →
  31. 31.3x − 4y = −5 and 6x + 6y = 60 →
  32. 32.2x + 3y = −20 and 3x + 2y = −15 →
  33. 33.x + 9y = 3 and 9x + y = −53 →
  34. 34.4x + 4y = 40 and 2x + y = 18 →
  35. 35.6x + 2y = −26 and 2x + 6y = 18 →
  36. 36.3x + 3y = −24 and 3x + y = −26 →
  37. 37.4x + 5y = 3 and 5x + y = −12 →
  38. 38.4x + 6y = 16 and x + y = 3 →
  39. 39.5x + 8y = −27 and 8x + 5y = −12 →
  40. 40.3x + y = 6 and x + 3y = 26 →

Answer key

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

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