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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 279 · 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. 1.3x + 5y = −25 and 5x + 3y = 1 →
  2. 2.x + 5y = −6 and 3x + 6y = 9 →
  3. 3.x + 8y = −47 and 8x + y = 2 →
  4. 4.3x + y = 8 and x + 3y = 8 →
  5. 5.5x + y = 30 and 3x + y = 16 →
  6. 6.8x + 4y = 88 and 4x + 8y = 80 →
  7. 7.x + 2y = 18 and 4x + y = 37 →
  8. 8.5x + 4y = −8 and 2x − 3y = −17 →
  9. 9.6x + 6y = 66 and 4x − 2y = 14 →
  10. 10.x − 2y = 10 and 2x + 5y = −16 →
  11. 11.2x − 3y = −13 and 4x + 4y = 4 →
  12. 12.2x + 2y = 0 and x + 6y = 40 →
  13. 13.x + 3y = 20 and 5x + 4y = 45 →
  14. 14.5x + 3y = 3 and 3x − 5y = −39 →
  15. 15.6x + 5y = 11 and 4x + 6y = 10 →
  16. 16.4x + 2y = −12 and 3x + 2y = −11 →
  17. 17.6x + 5y = 64 and 3x + 6y = 60 →
  18. 18.5x + y = 21 and 5x + 5y = 45 →
  19. 19.3x + y = 31 and 4x + 2y = 46 →
  20. 20.x − 3y = −20 and 5x + 3y = 26 →
  21. 21.4x + 6y = −4 and 6x + 6y = −12 →
  22. 22.6x − y = 21 and 2x + 5y = −41 →
  23. 23.3x + 6y = 54 and 6x + 3y = 63 →
  24. 24.3x + y = 19 and x + 3y = 9 →
  25. 25.7x + 2y = 17 and 2x + 7y = −53 →
  26. 26.4x + y = −25 and x + 4y = 5 →
  27. 27.6x + y = −10 and x − y = −4 →
  28. 28.6x + y = 43 and 3x + 3y = 39 →
  29. 29.6x + 3y = −27 and 3x + 6y = −9 →
  30. 30.4x + 7y = −6 and 7x + 4y = −27 →
  31. 31.x + 5y = −16 and x + y = 4 →
  32. 32.3x + 3y = 9 and 2x + y = 12 →
  33. 33.5x + 2y = 39 and 2x + 2y = 12 →
  34. 34.6x + 6y = −54 and 6x − 6y = 6 →
  35. 35.5x + 6y = 47 and 6x + 5y = 52 →
  36. 36.6x + 2y = 30 and x + y = 11 →
  37. 37.6x + 2y = 46 and 2x + 3y = 34 →
  38. 38.8x + y = −62 and x + 8y = 8 →
  39. 39.3x − y = 12 and 4x + 5y = 54 →
  40. 40.4x − y = 33 and x + y = 2 →

Answer key

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

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