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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 300 · 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. 1.5x + 8y = 4 and 8x + 5y = 22 →
  2. 2.2x + 3y = 5 and 5x + 5y = 15 →
  3. 3.4x − y = 28 and 4x + y = 44 →
  4. 4.x + 7y = −58 and 7x + y = 26 →
  5. 5.4x + 6y = 8 and x − 5y = −11 →
  6. 6.5x + 2y = −55 and 2x + 5y = −43 →
  7. 7.3x + 6y = 18 and 6x − y = 10 →
  8. 8.6x − 2y = −24 and 3x + 3y = 0 →
  9. 9.x + 6y = −43 and 6x + y = 22 →
  10. 10.4x + y = 24 and 3x + 6y = 39 →
  11. 11.2x + 3y = 22 and 3x + 5y = 34 →
  12. 12.2x + 2y = 8 and 4x + 2y = 10 →
  13. 13.3x + 5y = −2 and 2x + y = 1 →
  14. 14.7x + y = 66 and x + 7y = 30 →
  15. 15.8x + 3y = −17 and 3x + 8y = −27 →
  16. 16.4x + 3y = 15 and x + 4y = 33 →
  17. 17.5x − 4y = 4 and 4x + y = 41 →
  18. 18.3x − y = −16 and 2x + 5y = −56 →
  19. 19.4x + 5y = 2 and 5x + 4y = −2 →
  20. 20.4x + 8y = 56 and 8x + 4y = 64 →
  21. 21.8x + y = 21 and x + 8y = −21 →
  22. 22.2x + 3y = −4 and 5x + 6y = −4 →
  23. 23.3x − 2y = 19 and 6x + 5y = 20 →
  24. 24.x + 4y = 11 and 4x + y = 14 →
  25. 25.x + 3y = 10 and 3x + y = 6 →
  26. 26.x + y = 12 and 4x + 3y = 41 →
  27. 27.2x + 4y = −10 and 3x + 4y = −19 →
  28. 28.x + 6y = 15 and 4x + 2y = 16 →
  29. 29.3x + 4y = 36 and 4x + 3y = 34 →
  30. 30.5x + 4y = 11 and 5x + 5y = 10 →
  31. 31.8x + 2y = 6 and 2x + 8y = 54 →
  32. 32.6x − y = −19 and 6x − 5y = −47 →
  33. 33.3x + 5y = 36 and 2x − 5y = −26 →
  34. 34.x + y = −5 and 3x − 5y = 49 →
  35. 35.5x + 6y = 8 and x − y = −5 →
  36. 36.x − 4y = −23 and 2x − 4y = −22 →
  37. 37.x + 4y = −21 and 4x + y = −9 →
  38. 38.5x − 3y = −22 and 5x − y = −24 →
  39. 39.4x + 8y = 44 and 8x + 4y = 28 →
  40. 40.4x + y = 9 and 3x + y = 5 →

Answer key

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

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