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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 194 · 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. 1.9x + 4y = −60 and 4x + 9y = −5 →
  2. 2.5x + y = 21 and x + y = 9 →
  3. 3.x − 5y = 19 and 5x + 6y = 33 →
  4. 4.6x − 2y = 30 and 3x + 3y = 39 →
  5. 5.5x + 3y = 24 and x − 6y = −15 →
  6. 6.7x + y = −47 and x + 7y = 55 →
  7. 7.x − 5y = −9 and 6x + 2y = 42 →
  8. 8.5x + 5y = −30 and 3x + 6y = −45 →
  9. 9.x + 2y = 12 and 3x + 2y = 28 →
  10. 10.5x − 6y = 27 and 6x − 4y = 42 →
  11. 11.6x + 4y = 0 and 4x − y = 33 →
  12. 12.6x + 8y = 16 and 8x + 6y = −2 →
  13. 13.5x + 3y = −19 and 6x − 5y = 3 →
  14. 14.6x − 2y = −70 and 2x − 5y = −58 →
  15. 15.9x + 4y = −45 and 4x + 9y = 45 →
  16. 16.x − 3y = −20 and x + 2y = 25 →
  17. 17.5x − 6y = −41 and 4x + 3y = −25 →
  18. 18.3x + 4y = 45 and x + 6y = 57 →
  19. 19.5x + 6y = 27 and 6x + 5y = 39 →
  20. 20.2x + 3y = 37 and 3x + 2y = 38 →
  21. 21.4x + 5y = 17 and 6x + 3y = 3 →
  22. 22.2x + 4y = 6 and 4x + 2y = 6 →
  23. 23.5x − 2y = −34 and 3x − y = −20 →
  24. 24.5x + 4y = 38 and 4x − 6y = −34 →
  25. 25.x + 4y = −31 and 2x − 4y = 34 →
  26. 26.6x − 5y = −44 and 2x − 3y = −20 →
  27. 27.3x + 2y = 36 and x + 2y = 20 →
  28. 28.3x − 4y = 27 and 6x + 4y = −18 →
  29. 29.x − 6y = 3 and x + 2y = −5 →
  30. 30.7x + 6y = −27 and 6x + 7y = −38 →
  31. 31.x + 6y = −53 and x + 5y = −44 →
  32. 32.3x − 2y = 3 and 3x + 2y = 27 →
  33. 33.3x + y = −9 and 6x − 6y = 6 →
  34. 34.4x + 3y = 34 and 4x − 6y = −20 →
  35. 35.2x + 3y = 15 and 3x + 2y = 25 →
  36. 36.6x + 6y = 48 and 2x + 4y = 22 →
  37. 37.9x + 8y = −36 and 8x + 9y = −49 →
  38. 38.5x + 7y = −28 and 7x + 5y = −44 →
  39. 39.5x + 6y = 84 and x + 2y = 24 →
  40. 40.6x − 6y = −78 and 3x + 2y = −14 →

Answer key

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

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