Question

find the value of k, 2x+3y=4 and (k+2)x+6y=3k+2 will have infinitely many solutions

Answer 1

hope it will be helpful to you

Answer 2

In infinitely many solution the ratio of coefficient of ax^2+by-c and a'x^2+b'y=c' are equal.
so, 2/(k+2) = 3/6 = 4/(3k+2)
=> 2/(k+2) = 3/6
=> 2/(k+2) = 1/2
=> k+2 = 4
=> k = 4-2 = 2
hence, value of k = 2