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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 664 · 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.x + 3y = 10 and 5x + y = −34 →
  2. 2.6x + 2y = −12 and 5x + 5y = −40 →
  3. 3.2x + 5y = −19 and 3x − y = 31 →
  4. 4.5x − 3y = 25 and 6x + 2y = 58 →
  5. 5.4x + 3y = 14 and 6x + 5y = 18 →
  6. 6.2x + y = 1 and 5x + 2y = 4 →
  7. 7.7x + 3y = 58 and 3x + 7y = 42 →
  8. 8.3x + 2y = −4 and x − y = 7 →
  9. 9.2x + 6y = 22 and 3x − 5y = −9 →
  10. 10.x + 8y = −26 and 8x + y = −19 →
  11. 11.5x + 4y = 39 and 3x − 4y = −15 →
  12. 12.2x + 3y = 18 and x + 4y = 14 →
  13. 13.5x + 4y = 17 and 2x + y = 5 →
  14. 14.x + 3y = 15 and 6x + y = 56 →
  15. 15.6x + 9y = 75 and 9x + 6y = 60 →
  16. 16.5x + 2y = 27 and 2x + y = 11 →
  17. 17.9x + 7y = −17 and 7x + 9y = −31 →
  18. 18.x + 2y = 1 and 2x + y = −7 →
  19. 19.7x + 4y = 73 and 4x + 7y = 70 →
  20. 20.9x + 2y = −13 and 2x + 9y = −20 →
  21. 21.x + 4y = 25 and 4x + 6y = 60 →
  22. 22.5x + 5y = 5 and 6x + 2y = 22 →
  23. 23.3x + 5y = −9 and 5x − 5y = 25 →
  24. 24.6x + 2y = 46 and 2x + 6y = 26 →
  25. 25.x + 2y = 13 and 6x − 3y = −27 →
  26. 26.6x + y = 58 and x + 4y = 25 →
  27. 27.3x + 2y = 4 and 3x − y = 25 →
  28. 28.6x − 6y = 24 and 3x − 5y = 18 →
  29. 29.8x + y = −66 and x + 8y = −24 →
  30. 30.5x + y = 27 and 4x + 2y = 24 →
  31. 31.2x + 5y = 0 and 5x + 2y = −21 →
  32. 32.6x + 5y = −16 and x + 5y = −11 →
  33. 33.4x + y = −21 and x + 4y = 21 →
  34. 34.6x + 4y = −48 and 4x + 6y = −42 →
  35. 35.3x + 4y = −37 and x + 4y = −31 →
  36. 36.6x + 4y = −28 and 4x + 6y = −2 →
  37. 37.3x + y = 11 and 2x + 6y = 34 →
  38. 38.x + 9y = −14 and 9x + y = −46 →
  39. 39.5x − y = 8 and 5x − 3y = −6 →
  40. 40.3x − 4y = 23 and x + 5y = 14 →

Answer key

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

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