text: or
  
  # For which value (s) of lambda, do the pair of linear equations lambdax + y = lambda^(2) and x + lambda y = 1 have <br> (i) no solution ? (ii) infinitely many solutions ? <br> (iii) a unique solution ?
  
  Question from  Class 10  Chapter Pair Of Linear Equations In Two Variables
  
  Apne doubts clear karein ab Whatsapp par bhi. Try it now.
  CLICK HERE
  
  Loading DoubtNut Solution for you
  
  Watch 1000+ concepts & tricky questions explained!
  
  6.6 K+ views | 6.6 K+ people like this
  
  Share
  Share
  
  Answer Text
  
  Solution :
  The given pair of linear equations is <br> `lambdax + y = lambda^(2)` and `x + lambda y = 1` <br> Here, `" " a_(1) = lambda, b_(1) = 1, c_(1) = - lambda^(2)` <br> `a_(2) = 1, b_(2) = lambda, c_(2) = -1` <br> (i) For no solution, <br> `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) != (c_(1))/(c_(2))` <br> `rArr " " (lambda)/(1) = (1)/(lambda) != (-lambda^(2))/(-1)` <br> `rArr " " lambda^(2) - 1 = 0` <br> `rArr " " (lambda - 1) (lambda + 1) = 0` <br> `rArr " " lambda = 1, -1` <br> Here, we take only `lambda = -1` because at `lambda = 1` the system of linear equations has infinitely many solutions. <br> (ii) For infinitely many solutions, <br> `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))` <br> `rArr " " (lambda)/(1) = (1)/(lambda) = (lambda^(2))/(1)` <br> `rArr " " (lambda)/(1) = (lambda^(2))/(1)` <br> `rArr " " lambda (lambda - 1) = 0` <br> when `lambda != 0, ` then ` lambda = 1` <br> For a unique solution, <br> ` (a_(1))/(a_(2))!=(b_(1))/(b_(2)) rArr (lambda)/(1) != (1)/(lambda)` <br> `rArr " " lambda^(2) != 1 rArr lambda != +- 1` <br> So, all real values of `lambda ` except `+-1`.
  
  Related Video
  
  2:05
  
  60.2 K+ Views | 231.6 K+ Likes
  
  2:11
  
  500+ Views | 58.1 K+ Likes
  
  9:10
  
  400+ Views | 300+ Likes
  
  1:00
  
  30.5 K+ Views | 92.1 K+ Likes
  
  4:05
  
  67.1 K+ Views | 201.1 K+ Likes
  
  2:50
  
  41.7 K+ Views | 13.1 K+ Likes
  
  1:26
  
  134.0 K+ Views | 480.3 K+ Likes
metadata: {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}