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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 655 · 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. 1.2x − y = −10 and 4x + 5y = 36 →
  2. 2.3x + 2y = 26 and 2x + 3y = 29 →
  3. 3.x − 2y = −11 and 5x − 2y = 9 →
  4. 4.2x + 3y = −9 and x + 3y = −12 →
  5. 5.5x + 4y = 73 and 2x + 6y = 60 →
  6. 6.3x + 4y = 43 and 6x + 2y = 44 →
  7. 7.x − 5y = −32 and 6x + 2y = 0 →
  8. 8.6x + y = 38 and 5x + 5y = 65 →
  9. 9.x − 3y = −30 and 3x + y = −20 →
  10. 10.3x + 6y = 9 and 2x − 2y = 12 →
  11. 11.6x + 8y = 100 and 8x + 6y = 96 →
  12. 12.7x + 5y = 11 and 5x + 7y = 25 →
  13. 13.2x − 5y = −25 and x + 6y = 47 →
  14. 14.5x + 2y = 36 and 3x + 3y = 27 →
  15. 15.4x + 6y = −34 and 5x + 3y = −11 →
  16. 16.5x + 8y = 34 and 8x + 5y = 31 →
  17. 17.3x + 5y = 7 and 4x + 3y = 24 →
  18. 18.3x − 2y = 22 and 5x − 5y = 35 →
  19. 19.6x + y = 22 and x + 6y = −8 →
  20. 20.x − 6y = 2 and 4x + 2y = 34 →
  21. 21.8x + 2y = 34 and 2x + 8y = −44 →
  22. 22.x + 3y = 3 and 5x + 6y = 33 →
  23. 23.6x + y = −14 and x − y = −7 →
  24. 24.3x + 4y = 21 and 4x + 3y = 7 →
  25. 25.2x − 4y = −30 and 5x + y = 2 →
  26. 26.4x + 5y = 34 and x − y = 4 →
  27. 27.2x + 3y = 19 and 5x − y = 5 →
  28. 28.5x + 6y = −17 and x − y = 1 →
  29. 29.x − y = 16 and 5x + 6y = −19 →
  30. 30.4x + 4y = 12 and x + 6y = 8 →
  31. 31.2x + 2y = 20 and 5x + 4y = 48 →
  32. 32.4x + 4y = −36 and 3x + 2y = −26 →
  33. 33.3x + 2y = 16 and 2x − y = 6 →
  34. 34.x + 4y = 26 and 4x + y = 29 →
  35. 35.x + 7y = 17 and 7x + y = −25 →
  36. 36.4x + 2y = 2 and 2x + 4y = 10 →
  37. 37.6x + y = 51 and 4x − 5y = −17 →
  38. 38.8x + 7y = 60 and 7x + 8y = 60 →
  39. 39.x − y = 8 and 3x − 2y = 23 →
  40. 40.x + 3y = 29 and 3x + y = 15 →

Answer key

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

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