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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 313 · 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 + 8y = 58 and 8x + 2y = 82 →
  2. 2.8x + 3y = 21 and 3x + 8y = −54 →
  3. 3.6x − y = −60 and 6x + 5y = −24 →
  4. 4.9x + 2y = 9 and 2x + 9y = −75 →
  5. 5.5x + y = 8 and 5x − 6y = −13 →
  6. 6.4x + 2y = 30 and 6x + 6y = 72 →
  7. 7.5x + 9y = −42 and 9x + 5y = 14 →
  8. 8.2x + y = 3 and x + 2y = 3 →
  9. 9.7x + 5y = 22 and 5x + 7y = 26 →
  10. 10.3x + 4y = 43 and 6x + 2y = 62 →
  11. 11.6x + 3y = 48 and 3x − y = 14 →
  12. 12.9x + 6y = 123 and 6x + 9y = 117 →
  13. 13.x + 4y = 11 and 2x − 2y = 2 →
  14. 14.6x + 6y = 0 and x − 4y = −15 →
  15. 15.3x − 6y = 9 and 4x + 6y = 54 →
  16. 16.5x − 3y = −4 and 5x + y = 8 →
  17. 17.3x + 2y = −6 and 6x − y = 18 →
  18. 18.x − 5y = −2 and 3x + 5y = 34 →
  19. 19.7x + 3y = 34 and 3x + 7y = 26 →
  20. 20.5x + y = −22 and x + 5y = −14 →
  21. 21.4x − 2y = −42 and 6x + 4y = −42 →
  22. 22.x + 3y = 32 and 3x + y = 24 →
  23. 23.3x + y = 34 and x + 3y = 30 →
  24. 24.5x + 3y = 48 and 2x + 2y = 24 →
  25. 25.6x + y = −50 and x + 6y = −55 →
  26. 26.8x + 5y = −47 and 5x + 8y = −44 →
  27. 27.3x + 4y = −24 and x − y = −1 →
  28. 28.6x − 5y = 32 and 2x + y = 16 →
  29. 29.8x + 2y = −10 and 2x + 8y = 50 →
  30. 30.3x − y = 12 and x − 6y = −47 →
  31. 31.x + 5y = 13 and 2x + 6y = 14 →
  32. 32.6x − 4y = 50 and 4x + 3y = 39 →
  33. 33.2x − 2y = 6 and 3x + 5y = 41 →
  34. 34.3x + 4y = −31 and 5x − y = −21 →
  35. 35.5x + y = −29 and x + 4y = −21 →
  36. 36.5x + 4y = 10 and 4x + 5y = 17 →
  37. 37.6x + 4y = −4 and 4x + 6y = 4 →
  38. 38.6x + 7y = −20 and 7x + 6y = −19 →
  39. 39.6x − 5y = 44 and 5x + 3y = 8 →
  40. 40.x + 2y = 9 and 4x − 6y = 8 →

Answer key

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

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