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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 725 · 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. 1.6x − y = 22 and 5x + 2y = 24 →
  2. 2.3x + 6y = 33 and 6x + 3y = 21 →
  3. 3.6x + y = 24 and 3x + 2y = 21 →
  4. 4.2x + 4y = 40 and 3x + y = 15 →
  5. 5.x + 7y = −35 and 7x + y = −53 →
  6. 6.4x − 6y = −66 and x − 3y = −30 →
  7. 7.x + 6y = 24 and 3x + y = −13 →
  8. 8.6x + 6y = 60 and 2x − 5y = 13 →
  9. 9.x + 6y = −34 and x + 5y = −27 →
  10. 10.3x + 2y = −25 and 2x + 3y = −25 →
  11. 11.8x + 4y = −48 and 4x + 8y = −60 →
  12. 12.9x + 8y = 70 and 8x + 9y = 66 →
  13. 13.4x + 5y = 47 and 4x + y = 35 →
  14. 14.x + 4y = 26 and 6x + 6y = 66 →
  15. 15.7x + 8y = 59 and 8x + 7y = 61 →
  16. 16.6x + y = 43 and x − y = −1 →
  17. 17.5x − 2y = 50 and 2x + 5y = −9 →
  18. 18.9x + 4y = 8 and 4x + 9y = −47 →
  19. 19.2x + 9y = 73 and 9x + 2y = 59 →
  20. 20.6x + 6y = 66 and 4x − y = 9 →
  21. 21.4x + 3y = 11 and 3x + 4y = −4 →
  22. 22.4x − y = −41 and 5x + 4y = −4 →
  23. 23.5x + 6y = 40 and 5x + 2y = 20 →
  24. 24.2x + 5y = −42 and x + y = −9 →
  25. 25.4x − 2y = −20 and 5x − 4y = −31 →
  26. 26.6x + 4y = 58 and 6x + 3y = 57 →
  27. 27.x + 3y = 26 and 3x + y = 22 →
  28. 28.3x + 4y = 12 and 4x + 3y = −5 →
  29. 29.2x + 4y = 28 and 4x + 2y = 38 →
  30. 30.5x − y = −34 and 3x − 2y = −12 →
  31. 31.5x + y = 15 and 4x + 3y = 1 →
  32. 32.2x + 5y = −22 and x + 2y = −10 →
  33. 33.9x + 5y = −12 and 5x + 9y = −44 →
  34. 34.2x + 5y = −41 and 5x + 2y = −50 →
  35. 35.5x + 5y = 35 and 5x + y = 31 →
  36. 36.5x + 6y = 57 and 5x + 3y = 51 →
  37. 37.6x + 2y = 4 and 5x + 5y = −20 →
  38. 38.9x + y = 70 and x + 9y = −10 →
  39. 39.x + 2y = 16 and 2x + y = 5 →
  40. 40.7x + 2y = 65 and 2x + 7y = 70 →

Answer key

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

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