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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 447 · 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 + 2y = 16 and x + 6y = 18 →
  2. 2.4x + 2y = 20 and 6x + 6y = 48 →
  3. 3.5x + 2y = 56 and 3x − 4y = −8 →
  4. 4.5x + 4y = 45 and 4x + 5y = 45 →
  5. 5.4x + 3y = −51 and 4x − 4y = 12 →
  6. 6.3x + 8y = −8 and 8x + 3y = 52 →
  7. 7.2x + 5y = 9 and 5x + 2y = −9 →
  8. 8.6x − 3y = 0 and 2x − 5y = 8 →
  9. 9.4x + y = −17 and 3x + 5y = 0 →
  10. 10.x + 2y = 7 and 4x + 6y = 26 →
  11. 11.3x + 6y = −9 and 6x + 3y = −45 →
  12. 12.9x + 7y = −56 and 7x + 9y = −40 →
  13. 13.5x + 6y = −34 and 5x − 2y = 38 →
  14. 14.2x − y = −16 and 6x + 4y = −62 →
  15. 15.x + y = −10 and 6x + 3y = −45 →
  16. 16.6x − 5y = 11 and x − 3y = −9 →
  17. 17.6x + 3y = 48 and 3x + 6y = 15 →
  18. 18.6x + 4y = −6 and 5x − 4y = 17 →
  19. 19.3x + 6y = −3 and x + 3y = −3 →
  20. 20.2x − 2y = 26 and x + 6y = −36 →
  21. 21.2x + 5y = −11 and x + 4y = −10 →
  22. 22.x + 2y = 8 and 2x − 2y = 10 →
  23. 23.2x + 2y = 20 and 5x − 2y = 29 →
  24. 24.3x + 3y = 24 and 6x − 6y = −36 →
  25. 25.4x + 6y = 2 and 6x + 4y = −2 →
  26. 26.9x + 8y = −92 and 8x + 9y = −95 →
  27. 27.2x + 5y = 51 and 5x + 2y = 33 →
  28. 28.3x − 4y = −14 and x − 5y = −12 →
  29. 29.5x + y = −19 and 3x − 2y = −14 →
  30. 30.5x − y = −43 and 5x − 3y = −49 →
  31. 31.4x + 5y = 2 and 5x + 4y = 16 →
  32. 32.x + 5y = 32 and 6x + 4y = 10 →
  33. 33.8x + 6y = 30 and 6x + 8y = 26 →
  34. 34.3x − 2y = 12 and 2x + 4y = −8 →
  35. 35.6x − 2y = −6 and 2x + 6y = −42 →
  36. 36.6x + 3y = 33 and 3x + 6y = 39 →
  37. 37.3x + 4y = 30 and 4x + 3y = 26 →
  38. 38.4x + y = 15 and x + 4y = 15 →
  39. 39.6x + y = 9 and 4x − 3y = −5 →
  40. 40.3x − 6y = −18 and 2x − 3y = −8 →

Answer key

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

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