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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 832 · 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. 1.8x + 2y = 26 and 2x + 8y = 44 →
  2. 2.9x + 6y = 84 and 6x + 9y = 66 →
  3. 3.x + 6y = −9 and 4x − 2y = 42 →
  4. 4.7x + 5y = −6 and 5x + 7y = −18 →
  5. 5.6x + 4y = −20 and 4x + 6y = 0 →
  6. 6.x + 6y = 58 and 6x − 5y = −21 →
  7. 7.8x + 6y = −34 and 6x + 8y = −22 →
  8. 8.x − 6y = −41 and 6x + 3y = 66 →
  9. 9.9x + 3y = 6 and 3x + 9y = −54 →
  10. 10.8x + 3y = 58 and 3x + 8y = 63 →
  11. 11.x + 2y = −2 and 2x + y = 11 →
  12. 12.2x + 6y = 32 and 5x − 5y = −80 →
  13. 13.5x + 6y = 17 and 5x − 2y = 41 →
  14. 14.7x + 3y = 14 and 3x + 7y = −34 →
  15. 15.x + 6y = 45 and 6x + y = 60 →
  16. 16.6x + 2y = −10 and 2x − 6y = 10 →
  17. 17.3x + y = 29 and 2x − y = 6 →
  18. 18.x + 7y = 58 and 7x + y = −26 →
  19. 19.9x + 4y = −33 and 4x + 9y = 7 →
  20. 20.6x + 5y = 3 and 5x + 3y = −8 →
  21. 21.3x − 5y = −36 and 2x + 5y = 1 →
  22. 22.5x + y = 51 and 5x − 5y = 15 →
  23. 23.6x − 5y = 70 and 6x + y = 22 →
  24. 24.4x − 6y = −30 and 3x + 4y = 37 →
  25. 25.8x + 3y = 43 and 3x + 8y = −32 →
  26. 26.4x + 5y = 14 and 5x + 4y = 13 →
  27. 27.5x + 8y = −89 and 8x + 5y = −80 →
  28. 28.4x − y = 18 and 6x + 6y = 12 →
  29. 29.6x + 6y = 30 and 5x + y = −11 →
  30. 30.2x − y = −21 and x − 5y = −51 →
  31. 31.6x − 6y = −12 and x + 2y = 16 →
  32. 32.8x + 6y = 18 and 6x + 8y = −18 →
  33. 33.2x − 6y = 42 and 5x − 6y = 60 →
  34. 34.3x − y = −16 and 5x + 2y = −45 →
  35. 35.7x + 4y = 30 and 4x + 7y = 36 →
  36. 36.4x + 4y = 12 and 2x − 3y = 1 →
  37. 37.x + 6y = 19 and 6x + y = 44 →
  38. 38.5x + y = 32 and x + 5y = 16 →
  39. 39.5x + 5y = 5 and 5x + 6y = −3 →
  40. 40.6x + 7y = 68 and 7x + 6y = 75 →

Answer key

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

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