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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 943 · 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. 1.6x + y = 51 and x + 6y = 61 →
  2. 2.2x + 2y = −8 and 4x − 6y = 64 →
  3. 3.x + 9y = −24 and 9x + y = −56 →
  4. 4.x + 4y = 27 and 5x + y = −17 →
  5. 5.7x + 5y = 68 and 5x + 7y = 76 →
  6. 6.5x + 4y = 3 and 4x + 5y = −12 →
  7. 7.3x + 6y = −45 and 4x + 4y = −32 →
  8. 8.2x − 3y = −12 and 3x + y = −29 →
  9. 9.5x + 4y = 31 and 6x + 6y = 42 →
  10. 10.8x + y = 17 and x + 8y = −53 →
  11. 11.5x − y = −34 and 5x − 3y = −52 →
  12. 12.7x + 6y = −62 and 6x + 7y = −68 →
  13. 13.4x + 5y = 4 and 5x + y = −16 →
  14. 14.x + 6y = −12 and 3x − 4y = 30 →
  15. 15.3x + 4y = 26 and 4x + 4y = 24 →
  16. 16.3x − y = 9 and 2x − 3y = −8 →
  17. 17.x + 8y = 12 and 8x + y = 33 →
  18. 18.4x + 4y = −52 and 5x + 2y = −44 →
  19. 19.5x + 7y = −29 and 7x + 5y = −7 →
  20. 20.x + 4y = 31 and 6x − y = 36 →
  21. 21.3x + 9y = 48 and 9x + 3y = 72 →
  22. 22.8x + 9y = −6 and 9x + 8y = 6 →
  23. 23.4x + 7y = −11 and 7x + 4y = −11 →
  24. 24.5x + 8y = 33 and 8x + 5y = 6 →
  25. 25.4x + y = 13 and x + 4y = 7 →
  26. 26.x + 6y = 28 and 6x + y = 28 →
  27. 27.4x − 4y = −48 and 4x + 3y = 1 →
  28. 28.5x + 6y = 14 and 5x + 2y = −2 →
  29. 29.4x + 4y = −8 and 6x + y = −22 →
  30. 30.x + 6y = 21 and x + 5y = 19 →
  31. 31.4x − 2y = 28 and 4x + 5y = −14 →
  32. 32.5x + 3y = 17 and 5x + 2y = 23 →
  33. 33.4x + 4y = 44 and 5x + 6y = 64 →
  34. 34.4x − 3y = 13 and 6x + 4y = −6 →
  35. 35.3x + 7y = 44 and 7x + 3y = 36 →
  36. 36.5x − 6y = −2 and 4x − 4y = 4 →
  37. 37.4x + y = −26 and 4x + 4y = −8 →
  38. 38.x − 4y = −45 and 2x − y = −27 →
  39. 39.x + 7y = 1 and 7x + y = −41 →
  40. 40.2x + 5y = −17 and 5x + 2y = 10 →

Answer key

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

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