Question

2 X + 3 Y = 7 and (K + 2) x - 3 (1- k) y = 5 k + 1 .find the value of k, will the following pair of equations have infinitly many solution.
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Answer 1

For infinitely many solutions both the equations have a common factor among each other. The graph is a single line. using the same concept we can say,

2x + 3y = 7

(k+2)x - (1-k)y = 5k+1

let us say, common factor is p

then 2x = p(k+2)x

== pk+ 2p = 2

similarly

3y= -(1-k)yp

== kp - p = 3

comparing both equation we get

p = -1/3

k=-8