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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 212 · 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 + 9y = 83 and 9x + 5y = 71 →
  2. 2.7x + 4y = 48 and 4x + 7y = 18 →
  3. 3.2x − y = −5 and 3x + 5y = 51 →
  4. 4.3x − 2y = 22 and x + 5y = −21 →
  5. 5.4x + 6y = −22 and 6x + 3y = 21 →
  6. 6.3x + 8y = −40 and 8x + 3y = 40 →
  7. 7.3x + 6y = −30 and x + 6y = −42 →
  8. 8.5x + 6y = 82 and 6x + 5y = 83 →
  9. 9.6x + 9y = −39 and 9x + 6y = −36 →
  10. 10.6x − y = 8 and 3x + y = 1 →
  11. 11.x + 4y = 2 and 2x + y = −3 →
  12. 12.x + 6y = 44 and 4x − 5y = −27 →
  13. 13.4x − 5y = 71 and 4x + 4y = 8 →
  14. 14.x + 9y = 73 and 9x + y = 17 →
  15. 15.x + 2y = −20 and 2x + y = −19 →
  16. 16.3x + 2y = 25 and 2x + 3y = 30 →
  17. 17.x + y = −2 and x + 2y = 4 →
  18. 18.8x + 4y = 40 and 4x + 8y = −16 →
  19. 19.9x + 6y = 27 and 6x + 9y = 63 →
  20. 20.6x + 2y = 28 and 5x + 4y = 28 →
  21. 21.x − 6y = −16 and 2x + 3y = 13 →
  22. 22.5x − 5y = −80 and 6x + 3y = −15 →
  23. 23.5x − 2y = 32 and 5x − 4y = 34 →
  24. 24.5x − 2y = 39 and 5x − 3y = 36 →
  25. 25.3x + 6y = −78 and 6x + 3y = −75 →
  26. 26.8x + 5y = 11 and 5x + 8y = 2 →
  27. 27.2x − 5y = 45 and 6x + 4y = 2 →
  28. 28.8x + 3y = −40 and 3x + 8y = −70 →
  29. 29.3x + 9y = 6 and 9x + 3y = 66 →
  30. 30.4x + 2y = 12 and 3x − 2y = −5 →
  31. 31.5x + 2y = 1 and 6x + 3y = 6 →
  32. 32.3x + y = 0 and x + 3y = 24 →
  33. 33.x + 2y = −10 and 2x + y = 4 →
  34. 34.2x + 4y = 38 and 5x − 5y = 20 →
  35. 35.4x + 3y = 22 and 3x + 4y = 20 →
  36. 36.6x + 2y = 8 and 2x + 6y = −8 →
  37. 37.3x + 7y = 11 and 7x + 3y = 39 →
  38. 38.5x − 4y = 1 and x + 2y = −25 →
  39. 39.x + y = 5 and 6x + 4y = 38 →
  40. 40.8x + y = 26 and x + 8y = −44 →

Answer key

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

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