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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 153 · 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.x − 3y = −13 and 4x + 3y = 53 →
  2. 2.x − 6y = −52 and 6x + y = 21 →
  3. 3.x + 9y = 56 and 9x + y = 24 →
  4. 4.3x − 2y = −6 and x − 2y = −14 →
  5. 5.3x − 2y = 9 and x + 6y = 23 →
  6. 6.4x + 6y = −50 and 5x + 5y = −45 →
  7. 7.9x + 4y = 23 and 4x + 9y = 3 →
  8. 8.7x + 2y = −42 and 2x + 7y = −57 →
  9. 9.2x + 6y = 20 and x − 6y = −26 →
  10. 10.8x + 6y = −78 and 6x + 8y = −90 →
  11. 11.x + 2y = 11 and 4x + 5y = 35 →
  12. 12.x − 3y = 17 and 4x − 6y = 50 →
  13. 13.9x + 2y = −56 and 2x + 9y = −21 →
  14. 14.2x + 2y = −8 and 3x + 6y = 3 →
  15. 15.9x + y = 31 and x + 9y = −41 →
  16. 16.3x + 3y = 12 and 2x − 3y = −17 →
  17. 17.x + y = 4 and 2x + 5y = 11 →
  18. 18.4x + y = 21 and x + 4y = 24 →
  19. 19.6x − 2y = −16 and 3x + 6y = 27 →
  20. 20.6x + 2y = −26 and 2x + 6y = 34 →
  21. 21.2x + 9y = −20 and 9x + 2y = −13 →
  22. 22.8x + 2y = 56 and 2x + 8y = 74 →
  23. 23.5x − 3y = −23 and 2x + 4y = −4 →
  24. 24.4x − 4y = −40 and 2x + y = −14 →
  25. 25.3x + y = 7 and 2x + 3y = −7 →
  26. 26.6x − 2y = 0 and 5x + 2y = 33 →
  27. 27.2x − 2y = −20 and 6x + 5y = 17 →
  28. 28.4x − y = −7 and 3x + 2y = 3 →
  29. 29.2x + 3y = 2 and 2x + 4y = −2 →
  30. 30.3x + 9y = 87 and 9x + 3y = 45 →
  31. 31.6x + 4y = 50 and 6x + 6y = 66 →
  32. 32.4x + 5y = 7 and 6x − 2y = 58 →
  33. 33.x + y = 4 and 2x + 3y = 7 →
  34. 34.7x + 8y = 5 and 8x + 7y = 10 →
  35. 35.6x + 3y = 66 and 6x − 6y = 30 →
  36. 36.3x + 5y = 12 and 5x + 3y = 4 →
  37. 37.9x + 2y = 70 and 2x + 9y = 84 →
  38. 38.3x + 4y = 14 and 4x + 6y = 20 →
  39. 39.x − 6y = 11 and 6x − 6y = −24 →
  40. 40.6x + 4y = −34 and 4x − 2y = −32 →

Answer key

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

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