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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 267 · 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 + 3y = 8 and 3x + y = 16 →
  2. 2.x + 2y = −6 and 6x + 4y = −44 →
  3. 3.5x + 3y = 26 and 3x + 5y = 38 →
  4. 4.6x + 3y = 9 and 4x + y = 1 →
  5. 5.5x + 9y = −20 and 9x + 5y = 20 →
  6. 6.4x + 6y = 38 and 6x + 6y = 42 →
  7. 7.x + 5y = −37 and 5x + y = 7 →
  8. 8.2x + 6y = 40 and x − y = 4 →
  9. 9.x + 2y = 7 and 2x + y = 2 →
  10. 10.5x + 5y = 20 and 3x + y = 6 →
  11. 11.3x − y = −16 and 4x + 4y = 0 →
  12. 12.5x + 3y = 44 and 3x + 2y = 27 →
  13. 13.6x − y = −2 and 4x + 3y = −16 →
  14. 14.2x + 2y = 12 and 5x − 5y = −60 →
  15. 15.8x + 2y = −6 and 2x + 8y = 36 →
  16. 16.6x + 2y = 20 and 2x + 2y = 12 →
  17. 17.6x + 2y = −36 and 4x + 5y = −35 →
  18. 18.3x + 7y = 55 and 7x + 3y = 35 →
  19. 19.4x + 7y = 33 and 7x + 4y = 33 →
  20. 20.6x + 5y = −24 and x − 6y = 37 →
  21. 21.3x + 5y = −38 and 5x + 3y = −26 →
  22. 22.6x + 3y = 6 and 2x + 4y = 26 →
  23. 23.2x + 6y = 52 and x + y = 10 →
  24. 24.8x + 4y = 24 and 4x + 8y = 60 →
  25. 25.4x + y = −5 and x + 4y = 10 →
  26. 26.2x + 2y = 12 and 4x − 3y = 3 →
  27. 27.6x + 2y = −28 and 2x + 6y = −36 →
  28. 28.2x + 9y = 66 and 9x + 2y = 66 →
  29. 29.5x + 4y = 47 and 5x − 2y = 29 →
  30. 30.x + 9y = −45 and 9x + y = 75 →
  31. 31.6x + 2y = 54 and 6x + y = 45 →
  32. 32.2x + 3y = −9 and 3x + 2y = −11 →
  33. 33.2x + y = 3 and x + 2y = 3 →
  34. 34.5x − 3y = 17 and x + 2y = 6 →
  35. 35.2x + 8y = 88 and 8x + 2y = 82 →
  36. 36.8x + 4y = 4 and 4x + 8y = −4 →
  37. 37.3x + y = 7 and 6x + y = 19 →
  38. 38.2x + 5y = 43 and 5x + 6y = 49 →
  39. 39.x + 3y = −27 and x − 3y = 15 →
  40. 40.3x + 4y = 2 and 4x + 3y = −9 →

Answer key

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

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