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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 205 · 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 + 6y = 20 and 6x + 3y = 0 →
  2. 2.x + y = 5 and 4x − y = 35 →
  3. 3.2x − 2y = −24 and 3x − 6y = −63 →
  4. 4.2x − y = −13 and 3x + y = −7 →
  5. 5.x + 3y = −4 and 4x − y = −3 →
  6. 6.2x + 2y = 18 and 2x + 3y = 24 →
  7. 7.5x + 3y = −9 and 3x + 5y = 1 →
  8. 8.x + 3y = 12 and x − 2y = 7 →
  9. 9.2x + 6y = 46 and 5x + 2y = 11 →
  10. 10.3x + 5y = 32 and 3x + 3y = 30 →
  11. 11.3x − 4y = −31 and x + 5y = 34 →
  12. 12.2x − 4y = −20 and 5x + y = −6 →
  13. 13.x + 2y = −6 and 5x + 5y = 5 →
  14. 14.6x + 5y = 0 and 3x + y = 9 →
  15. 15.3x + y = −27 and 6x + 5y = −81 →
  16. 16.2x + 2y = 16 and 4x + 3y = 30 →
  17. 17.2x + 2y = 16 and x − 4y = −7 →
  18. 18.6x + 6y = −36 and 6x + 4y = −20 →
  19. 19.5x + 5y = 30 and x − 2y = −15 →
  20. 20.3x − 5y = −34 and 4x − 6y = −40 →
  21. 21.5x + 4y = 56 and 4x + 5y = 61 →
  22. 22.x + 3y = 9 and 2x + 2y = 14 →
  23. 23.x − 2y = 13 and 2x + 2y = −10 →
  24. 24.2x + 6y = 14 and 6x + 2y = −6 →
  25. 25.x − y = 5 and 5x + 2y = 46 →
  26. 26.5x + 4y = −8 and 5x − 4y = −32 →
  27. 27.4x + 3y = −35 and 2x + y = −13 →
  28. 28.4x − 2y = 12 and 5x − 6y = 22 →
  29. 29.4x + 5y = −9 and 5x + 5y = 0 →
  30. 30.x + 5y = −8 and 3x + 5y = 6 →
  31. 31.7x + 5y = 36 and 5x + 7y = 36 →
  32. 32.7x + y = 13 and x + 7y = 43 →
  33. 33.x + y = 10 and 3x + y = 28 →
  34. 34.2x + 3y = 9 and 5x + 5y = 10 →
  35. 35.2x − 5y = 47 and x + 5y = −29 →
  36. 36.2x − 4y = −52 and x − 6y = −62 →
  37. 37.3x + 6y = −12 and 6x + 4y = 8 →
  38. 38.x + 5y = 28 and 6x + y = −35 →
  39. 39.3x − y = 6 and 6x + 6y = 60 →
  40. 40.x + y = 7 and 3x + 2y = 17 →

Answer key

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

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