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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 503 · 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. 1.5x + 5y = 45 and 4x − 3y = −13 →
  2. 2.x + 3y = 28 and x + 6y = 55 →
  3. 3.x + 2y = 5 and x + y = 3 →
  4. 4.6x + 5y = 87 and 6x − 6y = −12 →
  5. 5.6x + 5y = 4 and 2x − y = −4 →
  6. 6.6x − 3y = −69 and 6x + 2y = −24 →
  7. 7.8x + 2y = −58 and 2x + 8y = 8 →
  8. 8.x + 9y = −23 and 9x + y = 33 →
  9. 9.5x + y = −10 and 3x + 4y = −23 →
  10. 10.5x − 4y = 21 and 2x + 3y = 13 →
  11. 11.2x + 9y = 7 and 9x + 2y = 70 →
  12. 12.x + 4y = 12 and 3x − 5y = 19 →
  13. 13.4x + 2y = −30 and 6x + y = −31 →
  14. 14.2x + y = 5 and 4x + 3y = 17 →
  15. 15.6x − y = −34 and 6x + 5y = −82 →
  16. 16.9x + 5y = 14 and 5x + 9y = −42 →
  17. 17.3x + 3y = 0 and 6x + 4y = 12 →
  18. 18.4x − 4y = −8 and 5x + y = −4 →
  19. 19.2x − 2y = −22 and 3x + 3y = 15 →
  20. 20.2x − 2y = 10 and 6x + y = 2 →
  21. 21.6x + 5y = −22 and 3x + y = −8 →
  22. 22.2x + 4y = 26 and 2x − 5y = −46 →
  23. 23.2x − y = 9 and 3x + 5y = 20 →
  24. 24.5x − 2y = 3 and 6x + 4y = −54 →
  25. 25.3x + 5y = −34 and 5x + 3y = −30 →
  26. 26.3x + 6y = 9 and 4x + 5y = 9 →
  27. 27.3x + 7y = −19 and 7x + 3y = 9 →
  28. 28.7x + 3y = −68 and 3x + 7y = −52 →
  29. 29.5x − 2y = 17 and 2x − 4y = −22 →
  30. 30.4x − 4y = 44 and 6x + 2y = 10 →
  31. 31.x + 2y = −3 and x + 4y = 1 →
  32. 32.2x − 5y = 0 and 3x + 5y = 25 →
  33. 33.2x + 4y = −8 and 2x + 2y = 0 →
  34. 34.3x + y = 17 and x + 5y = 43 →
  35. 35.x + 2y = 15 and x + 4y = 29 →
  36. 36.2x − 4y = −32 and 6x + 2y = 30 →
  37. 37.9x + 3y = −24 and 3x + 9y = 48 →
  38. 38.3x + 6y = 45 and 2x + 6y = 40 →
  39. 39.2x + 8y = 28 and 8x + 2y = 22 →
  40. 40.5x + 5y = −25 and 2x − 4y = 8 →

Answer key

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

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