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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 383 · 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 − y = 9 and 5x − 3y = 43 →
  2. 2.2x + 7y = −2 and 7x + 2y = −52 →
  3. 3.x + 2y = −5 and 3x + 2y = 9 →
  4. 4.2x − 4y = 24 and 5x + 5y = 15 →
  5. 5.3x + y = −18 and 6x + y = −39 →
  6. 6.4x + 5y = 46 and 5x + 4y = 44 →
  7. 7.3x + 6y = 27 and 3x + 2y = 23 →
  8. 8.5x − y = 2 and 6x + y = 9 →
  9. 9.3x − 5y = 13 and x + y = 7 →
  10. 10.3x − 5y = −66 and 3x − 2y = −39 →
  11. 11.x + 4y = −9 and 2x − 2y = 22 →
  12. 12.3x + 6y = −21 and 2x + y = −11 →
  13. 13.6x + 5y = 51 and 3x + y = 21 →
  14. 14.5x + 3y = 44 and 2x − y = 0 →
  15. 15.4x + 8y = −20 and 8x + 4y = 20 →
  16. 16.7x + 3y = −71 and 3x + 7y = −59 →
  17. 17.2x + 5y = 29 and x − 3y = −2 →
  18. 18.8x + 3y = 30 and 3x + 8y = 25 →
  19. 19.x + 3y = 5 and 6x + 4y = −12 →
  20. 20.5x + y = 22 and x + 5y = 14 →
  21. 21.2x + 7y = −15 and 7x + 2y = −30 →
  22. 22.2x + 9y = 59 and 9x + 2y = 73 →
  23. 23.3x + 2y = 3 and 4x + y = 19 →
  24. 24.7x + 8y = 41 and 8x + 7y = 34 →
  25. 25.5x + 3y = −7 and 3x + 5y = −1 →
  26. 26.5x + 7y = 37 and 7x + 5y = 47 →
  27. 27.6x + 2y = −20 and 5x + 2y = −18 →
  28. 28.x + 2y = 0 and 6x + y = 22 →
  29. 29.5x + y = 29 and 5x − y = 41 →
  30. 30.5x + y = 21 and 5x + 5y = 45 →
  31. 31.5x + 7y = 44 and 7x + 5y = 52 →
  32. 32.5x + 4y = 25 and 2x + y = 7 →
  33. 33.8x + 7y = 23 and 7x + 8y = 37 →
  34. 34.9x + 7y = −22 and 7x + 9y = −10 →
  35. 35.x + 6y = 9 and 2x + y = −15 →
  36. 36.3x − y = 13 and 5x − 2y = 21 →
  37. 37.4x + 2y = 40 and 6x + 5y = 64 →
  38. 38.5x + 3y = 21 and 3x + 5y = 19 →
  39. 39.4x + 9y = −42 and 9x + 4y = 3 →
  40. 40.x + 7y = 62 and 7x + y = 50 →

Answer key

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

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