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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 438 · 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. 1.7x + y = 45 and x + 7y = 27 →
  2. 2.2x + 6y = 46 and 6x + 2y = 42 →
  3. 3.x + 6y = 10 and 6x + y = 25 →
  4. 4.2x + 4y = 20 and 2x + 6y = 26 →
  5. 5.x + y = 10 and 4x + 5y = 49 →
  6. 6.6x − 4y = 50 and 4x + y = 37 →
  7. 7.5x + y = −24 and 2x − y = 3 →
  8. 8.5x + y = 41 and 2x + 4y = 38 →
  9. 9.2x + 3y = −35 and x + y = −14 →
  10. 10.4x + 8y = −48 and 8x + 4y = −12 →
  11. 11.2x + 2y = −12 and 4x + 5y = −26 →
  12. 12.6x + 5y = −76 and 6x − 5y = 4 →
  13. 13.x + 5y = 4 and x − y = −2 →
  14. 14.6x + 2y = −32 and 2x + 6y = 32 →
  15. 15.x + 2y = −11 and 2x + y = −7 →
  16. 16.6x + y = 49 and x + 6y = 14 →
  17. 17.x + 5y = 10 and 5x + y = −22 →
  18. 18.x + 2y = −17 and 2x + y = −7 →
  19. 19.6x + 2y = 24 and 4x + 3y = 31 →
  20. 20.x + y = 11 and 4x − 4y = −28 →
  21. 21.9x + 6y = −27 and 6x + 9y = −63 →
  22. 22.3x − 2y = 26 and 2x + y = 1 →
  23. 23.5x + 7y = 68 and 7x + 5y = 52 →
  24. 24.4x + 4y = 16 and 5x + y = 32 →
  25. 25.6x + 2y = 50 and 5x + 5y = 65 →
  26. 26.3x + 3y = 12 and x − 2y = −20 →
  27. 27.4x + 4y = −28 and 2x − 5y = 28 →
  28. 28.6x − 4y = −12 and x + 6y = 58 →
  29. 29.x + 2y = 16 and 5x + 2y = 48 →
  30. 30.2x − 6y = 46 and 3x + 5y = −43 →
  31. 31.x + 6y = −34 and 6x + y = 41 →
  32. 32.4x − 4y = −20 and x + 4y = 25 →
  33. 33.2x + 3y = −5 and x + y = −3 →
  34. 34.3x − 3y = 36 and 4x − y = 24 →
  35. 35.3x + 6y = 30 and 5x + y = 32 →
  36. 36.x + 6y = 32 and 6x + y = 17 →
  37. 37.4x + 2y = 16 and 2x + 4y = −4 →
  38. 38.4x + y = 37 and x + 4y = 13 →
  39. 39.x + 6y = 36 and 6x + y = 41 →
  40. 40.5x + 2y = 16 and 2x + 5y = 19 →

Answer key

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

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