This is the basic and exam oriented question from linear equations in two variables in which we have given two equations 2x+(k-2)y=k, 6x+(2k-1)y=(2k+5) and we have been asked to find the value of k for which it has infinite solutions
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3D, question no 16
For the system to have infinitely many solutions, lines must coincide each other
⇒ratio of respective coefficients must be equal (x, y and constant coefficients)
⇒2/6=(k−2)/(2k-1)=k/(2k+5)
Equate first two equations ;
⇒2k−1=3k−6
⇒k=5