Q. 75.0( 2 Votes )

Show that the straight lines given by (2 + k)x + (1 + k)y = 5 + 7k for different values of k pass through a fixed point. Also, find that point.

Answer :

Given:


lines given by (2 + k)x + (1 + k)y = 5 + 7k


To prove:


The straight lines given by (2 + k)x + (1 + k)y = 5 + 7k for different values of k pass through a fixed point


Explanation:


The given straight line (2 + k)x + (1 + k)y = 5 + 7k can be written in the following way:


2x + y 5 + k (x + y 7) = 0


This line is of the form L1 + kL2 = 0, which passes through the intersection of the lines
L1 = 0 and L2 = 0, i.e. 2x + y
5 = 0 and x + y 7 = 0.


Solving 2x + y 5 = 0 and x + y 7 = 0, we get ( 2, 9), which is the fixed point.


Hence proved.


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