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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 348 · 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 + 3y = 8 and 3x + 6y = 9 →
  2. 2.6x − 4y = 30 and x − 3y = −9 →
  3. 3.x − y = −10 and 3x + 5y = 26 →
  4. 4.x − 2y = −23 and 6x + 5y = −2 →
  5. 5.6x − y = 32 and 4x + 2y = 0 →
  6. 6.x − y = 1 and 6x + 5y = −60 →
  7. 7.4x + 6y = 12 and 6x + 4y = −2 →
  8. 8.3x − 2y = −4 and 6x − 5y = −1 →
  9. 9.x + 6y = −55 and 2x + 5y = −47 →
  10. 10.3x + 2y = 14 and 2x + 3y = 16 →
  11. 11.x − 2y = 14 and 5x − 2y = 6 →
  12. 12.2x − 6y = −24 and 2x − 5y = −18 →
  13. 13.8x + 2y = 22 and 2x + 8y = 28 →
  14. 14.3x + 2y = 13 and x − 2y = 23 →
  15. 15.5x + 5y = 30 and 5x + y = 10 →
  16. 16.7x + 8y = 39 and 8x + 7y = 36 →
  17. 17.4x − y = 20 and 6x + 4y = 74 →
  18. 18.7x + 8y = 62 and 8x + 7y = 58 →
  19. 19.2x + 2y = 24 and 4x + 2y = 38 →
  20. 20.9x + 3y = 63 and 3x + 9y = 45 →
  21. 21.x + 4y = 30 and 5x − 2y = −4 →
  22. 22.2x + 5y = −41 and 5x + 4y = −43 →
  23. 23.2x − 5y = −57 and 4x + 3y = 3 →
  24. 24.2x + 3y = −1 and 3x + 4y = −3 →
  25. 25.4x − 2y = 4 and 4x + 4y = 16 →
  26. 26.4x + 2y = 22 and 3x + y = 15 →
  27. 27.x + y = −11 and 4x − 6y = −24 →
  28. 28.8x + 4y = −4 and 4x + 8y = 16 →
  29. 29.6x + 5y = −17 and x + 3y = 8 →
  30. 30.4x + 8y = −104 and 8x + 4y = −100 →
  31. 31.5x + 6y = −37 and 6x + 4y = −22 →
  32. 32.3x + 6y = −9 and 6x + 3y = 18 →
  33. 33.3x + 7y = −33 and 7x + 3y = −37 →
  34. 34.3x + 5y = −1 and 3x + y = −17 →
  35. 35.6x + 8y = 108 and 8x + 6y = 102 →
  36. 36.5x + 4y = −11 and 4x + 5y = −25 →
  37. 37.5x + y = 14 and 2x + 4y = 2 →
  38. 38.3x + 6y = 9 and 6x + 3y = −18 →
  39. 39.x + 5y = 43 and 6x + 4y = 24 →
  40. 40.x + y = 2 and x + 4y = 5 →

Answer key

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

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