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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 233 · 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. 1.7x + 8y = 106 and 8x + 7y = 104 →
  2. 2.5x + 6y = 56 and 2x + 3y = 26 →
  3. 3.5x − 5y = 0 and x + 2y = 27 →
  4. 4.x + 4y = 45 and 5x − 6y = −9 →
  5. 5.9x + 2y = 35 and 2x + 9y = 42 →
  6. 6.6x − y = −21 and x + 3y = 6 →
  7. 7.3x + 2y = 15 and 4x + 2y = 22 →
  8. 8.x + 3y = −18 and 3x + y = −14 →
  9. 9.x − 2y = −1 and 3x − 2y = −15 →
  10. 10.3x + 8y = −7 and 8x + 3y = −37 →
  11. 11.4x + 6y = 52 and 5x − y = 14 →
  12. 12.5x + 3y = 28 and 6x + 5y = 35 →
  13. 13.x − y = 1 and 5x + 5y = 35 →
  14. 14.6x − 6y = 6 and 6x + 6y = −90 →
  15. 15.6x + y = 19 and 6x − y = 5 →
  16. 16.x − 4y = 18 and x + 6y = −32 →
  17. 17.8x + 6y = 28 and 6x + 8y = 42 →
  18. 18.4x + 3y = 25 and 5x − 5y = 5 →
  19. 19.5x + 6y = 51 and 6x + 5y = 59 →
  20. 20.4x + 5y = −21 and 5x + 4y = −15 →
  21. 21.6x + 8y = −70 and 8x + 6y = −84 →
  22. 22.5x + 3y = 34 and 5x − 2y = 44 →
  23. 23.x − 3y = 15 and 5x + 6y = 33 →
  24. 24.3x + y = 25 and x + 3y = 19 →
  25. 25.9x + 6y = 42 and 6x + 9y = 48 →
  26. 26.6x + 4y = 42 and 4x + 4y = 32 →
  27. 27.9x + 6y = 60 and 6x + 9y = 75 →
  28. 28.2x + 9y = 4 and 9x + 2y = −59 →
  29. 29.x + 3y = 14 and 5x + 4y = 26 →
  30. 30.8x + y = −61 and x + 8y = 16 →
  31. 31.5x + 2y = 23 and 3x + 2y = 17 →
  32. 32.2x + 4y = 6 and x + y = 2 →
  33. 33.2x − y = 12 and x + 6y = −46 →
  34. 34.4x + 5y = 67 and 5x + 4y = 68 →
  35. 35.3x + 3y = −9 and 3x − 3y = −15 →
  36. 36.x + 6y = 32 and x + 4y = 22 →
  37. 37.5x + 5y = 0 and 2x + 3y = −4 →
  38. 38.x − y = −1 and 2x + 6y = 54 →
  39. 39.x + y = 13 and 3x + 5y = 47 →
  40. 40.2x + y = −3 and 5x + 6y = −39 →

Answer key

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

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