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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 798 · 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. 1.4x + y = 15 and 6x + 2y = 26 →
  2. 2.2x + 5y = 38 and 6x + 6y = 78 →
  3. 3.6x + 4y = 40 and 4x + 2y = 24 →
  4. 4.3x + y = 19 and x + 3y = 17 →
  5. 5.2x + 5y = 43 and 3x + 2y = 26 →
  6. 6.9x + 2y = 76 and 2x + 9y = 34 →
  7. 7.5x + y = 25 and 3x + 3y = 27 →
  8. 8.x + 2y = 13 and 6x + 2y = 48 →
  9. 9.2x − 3y = −31 and 6x + 2y = −38 →
  10. 10.6x + y = 8 and x + 6y = 13 →
  11. 11.2x − 3y = 15 and x − y = 8 →
  12. 12.6x + 4y = 10 and x + 6y = 23 →
  13. 13.2x − 3y = −10 and x + 6y = −20 →
  14. 14.2x + y = 8 and x + 2y = 7 →
  15. 15.5x + y = 51 and x + 5y = 39 →
  16. 16.4x + 2y = −18 and 5x − 2y = 9 →
  17. 17.6x + 8y = 84 and 8x + 6y = 70 →
  18. 18.3x + y = −13 and x + 3y = 1 →
  19. 19.3x − 5y = −38 and 2x − 3y = −23 →
  20. 20.4x + 4y = 40 and 2x + 3y = 24 →
  21. 21.3x + 6y = 51 and 6x + 3y = 30 →
  22. 22.3x + 2y = 26 and 2x + 3y = 29 →
  23. 23.6x + y = 19 and 4x + 2y = 14 →
  24. 24.2x + 6y = −24 and 5x + y = 38 →
  25. 25.6x + 5y = 22 and 6x − 2y = 8 →
  26. 26.4x + 5y = −34 and 3x + y = −9 →
  27. 27.x + y = −5 and 6x − y = −23 →
  28. 28.x − 3y = 19 and 3x + 4y = −60 →
  29. 29.x + 4y = −3 and 4x + y = 3 →
  30. 30.6x + 9y = 120 and 9x + 6y = 120 →
  31. 31.4x + 2y = 22 and 4x + 3y = 25 →
  32. 32.8x + 6y = 54 and 6x + 8y = 30 →
  33. 33.2x + 4y = −26 and 5x + 5y = −20 →
  34. 34.5x + 8y = −7 and 8x + 5y = 20 →
  35. 35.x + 4y = 27 and 5x + 3y = 33 →
  36. 36.2x + 8y = −6 and 8x + 2y = 66 →
  37. 37.6x − y = 46 and 2x + y = 26 →
  38. 38.6x + y = −10 and 6x + 3y = −6 →
  39. 39.2x + y = 0 and x + 2y = −12 →
  40. 40.7x + 6y = 43 and 6x + 7y = 48 →

Answer key

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

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