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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 272 · 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. 1.8x + 3y = 61 and 3x + 8y = 16 →
  2. 2.x + 4y = −14 and 2x + y = 0 →
  3. 3.2x − 6y = 58 and x − 5y = 47 →
  4. 4.6x + 5y = 45 and 6x − 2y = 24 →
  5. 5.3x + y = 35 and x + 5y = 49 →
  6. 6.x − y = 10 and 6x + 4y = 0 →
  7. 7.9x + 7y = −58 and 7x + 9y = −70 →
  8. 8.4x + 2y = 16 and 2x + 4y = −4 →
  9. 9.2x + 9y = −51 and 9x + 2y = 40 →
  10. 10.x − 5y = 36 and 5x + y = −2 →
  11. 11.5x − 4y = 17 and 2x − 3y = 4 →
  12. 12.x + 6y = −20 and 6x + y = −15 →
  13. 13.3x + 7y = 67 and 7x + 3y = 63 →
  14. 14.x + 3y = 1 and 3x + y = −21 →
  15. 15.3x + y = −35 and x + 3y = −33 →
  16. 16.7x + 3y = −29 and 3x + 7y = 39 →
  17. 17.x + 8y = 24 and 8x + y = 66 →
  18. 18.3x + 4y = −9 and 6x + 2y = 18 →
  19. 19.8x + 2y = 44 and 2x + 8y = −4 →
  20. 20.5x + 6y = 81 and 6x + 5y = 84 →
  21. 21.x + y = 11 and 5x + 6y = 57 →
  22. 22.x + 5y = 9 and 6x − 5y = 19 →
  23. 23.x − y = −9 and 5x + y = −27 →
  24. 24.3x + 6y = −36 and x − 5y = 51 →
  25. 25.x + 5y = 18 and x + y = 10 →
  26. 26.2x + 4y = 18 and 3x − 3y = 9 →
  27. 27.6x + 3y = 33 and x + 2y = 10 →
  28. 28.5x + 5y = −10 and x + 3y = 0 →
  29. 29.3x + 8y = −45 and 8x + 3y = −65 →
  30. 30.5x + 5y = 35 and 2x + 6y = 38 →
  31. 31.4x + y = 34 and 5x + y = 43 →
  32. 32.4x + 2y = 48 and 3x − 5y = −3 →
  33. 33.2x + y = 17 and 2x − 2y = 2 →
  34. 34.4x + 2y = −26 and x + 2y = −2 →
  35. 35.3x + 4y = 12 and 4x + 3y = −5 →
  36. 36.9x + 5y = 19 and 5x + 9y = 23 →
  37. 37.x + 5y = 7 and 5x + y = −37 →
  38. 38.3x + 2y = 28 and 2x + 3y = 27 →
  39. 39.6x + 3y = 39 and 2x + 4y = 10 →
  40. 40.4x + 6y = 10 and 6x + 3y = −15 →

Answer key

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

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