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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 79 · 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 x + 4y = 5 →
  2. 2.6x + y = 48 and 4x + 3y = 46 →
  3. 3.4x + 5y = 7 and 5x + 4y = −7 →
  4. 4.9x + 2y = 32 and 2x + 9y = −10 →
  5. 5.6x + 5y = 16 and x + 6y = 44 →
  6. 6.3x + 5y = −42 and 5x + 3y = −38 →
  7. 7.3x + 5y = 28 and 5x + 3y = 36 →
  8. 8.8x + 2y = 38 and 2x + 8y = −58 →
  9. 9.6x + 6y = −36 and 5x − y = 18 →
  10. 10.4x + 6y = 14 and 2x + 5y = 13 →
  11. 11.x + 5y = −26 and 5x + y = −10 →
  12. 12.9x + 7y = 96 and 7x + 9y = 96 →
  13. 13.3x + y = 33 and x + 3y = 35 →
  14. 14.x − 5y = −14 and 2x + 4y = 28 →
  15. 15.9x + 7y = 37 and 7x + 9y = 43 →
  16. 16.6x + 3y = 33 and 6x + 2y = 38 →
  17. 17.x + 8y = 20 and 8x + y = −29 →
  18. 18.8x + 7y = 4 and 7x + 8y = 11 →
  19. 19.4x − 2y = −24 and 2x + 4y = −2 →
  20. 20.6x + y = 21 and x + 6y = −49 →
  21. 21.6x − 4y = −84 and 2x − 2y = −34 →
  22. 22.2x + 5y = 5 and 2x + 2y = 8 →
  23. 23.4x + 5y = 38 and 5x + 4y = 43 →
  24. 24.3x + 5y = 0 and 6x + 2y = 24 →
  25. 25.2x + 6y = −28 and 4x + 4y = −16 →
  26. 26.3x + 5y = 41 and 4x + 2y = 36 →
  27. 27.5x + 4y = 3 and 2x + y = 0 →
  28. 28.3x − y = 14 and x − y = 2 →
  29. 29.x − 4y = −36 and 5x + 2y = −26 →
  30. 30.7x + 8y = 29 and 8x + 7y = 31 →
  31. 31.3x + 7y = −8 and 7x + 3y = 8 →
  32. 32.8x + 6y = 50 and 6x + 8y = 62 →
  33. 33.8x + 3y = 39 and 3x + 8y = 49 →
  34. 34.6x + y = 59 and 6x + 2y = 64 →
  35. 35.x + 4y = 18 and 4x + 4y = 36 →
  36. 36.6x − y = 30 and x + 2y = −8 →
  37. 37.2x + 2y = −2 and 3x − 4y = −45 →
  38. 38.8x + 5y = −2 and 5x + 8y = −11 →
  39. 39.4x + 5y = 4 and 6x + y = 32 →
  40. 40.6x − 5y = −64 and 6x + 6y = −42 →

Answer key

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

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