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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 61 · 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. 1.4x − 5y = 1 and 2x + y = 25 →
  2. 2.2x + 6y = −40 and 6x + y = −1 →
  3. 3.x − 5y = 34 and 2x − 5y = 43 →
  4. 4.4x + 9y = 5 and 9x + 4y = 60 →
  5. 5.3x + 3y = 0 and 4x + 3y = −1 →
  6. 6.9x + 7y = 51 and 7x + 9y = 61 →
  7. 7.x + 5y = 50 and 2x − 4y = −26 →
  8. 8.4x + 3y = −41 and 3x − y = −8 →
  9. 9.2x + 5y = 13 and 2x − y = 7 →
  10. 10.3x + 6y = −24 and 6x + 3y = −21 →
  11. 11.x + 6y = 32 and 6x + y = −18 →
  12. 12.6x + 5y = −6 and x − y = −12 →
  13. 13.2x + 2y = 0 and 4x + 6y = 4 →
  14. 14.5x − 4y = −61 and 4x + 3y = 7 →
  15. 15.5x + 6y = 51 and 6x + 5y = 48 →
  16. 16.x + 5y = 28 and 5x + y = 44 →
  17. 17.2x + 9y = 0 and 9x + 2y = 77 →
  18. 18.5x + y = 34 and x + 5y = 26 →
  19. 19.6x − 3y = −48 and 6x + 6y = 6 →
  20. 20.5x + 5y = 85 and x − 2y = −10 →
  21. 21.7x + 3y = −25 and 3x + 7y = 35 →
  22. 22.5x + 2y = 23 and 5x + y = 14 →
  23. 23.3x + 3y = 51 and 4x + 3y = 59 →
  24. 24.9x + 8y = 78 and 8x + 9y = 75 →
  25. 25.6x + 2y = 44 and x + 4y = 11 →
  26. 26.2x + 9y = 3 and 9x + 2y = 52 →
  27. 27.x − 3y = 28 and 6x + 6y = −24 →
  28. 28.6x + 5y = −6 and 3x + 3y = −6 →
  29. 29.2x − 4y = −14 and 5x − 6y = −3 →
  30. 30.2x + 5y = −36 and 6x + y = 4 →
  31. 31.6x + 2y = −20 and 2x + 6y = 20 →
  32. 32.6x + 3y = −15 and x + 4y = 22 →
  33. 33.2x − 6y = −10 and 6x − 6y = 18 →
  34. 34.2x + 7y = 33 and 7x + 2y = 48 →
  35. 35.9x + 4y = −51 and 4x + 9y = −1 →
  36. 36.x + 6y = 31 and 4x + y = 9 →
  37. 37.8x + 4y = −32 and 4x + 8y = −40 →
  38. 38.x + 2y = −11 and 5x + 4y = −31 →
  39. 39.x + 4y = 34 and 4x + y = 16 →
  40. 40.x − 3y = 20 and 5x + 2y = 32 →

Answer key

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

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