Question

7. For what value of k the following system of linear equations has a no solution?
x + 2y = 3
(k-1)x + (k + 1)y = k + 2​

Answer 1

Answer:

What is the number value of k for which the system of linear equations (k+1) x+8y=4k & kx+(k+3) y=3k-1 has infinite solutions?

For solution to have infinite solutions, ratio of x coefficients=ratio of y coefficients=ratio of constants

=>(k+1)/k=8/(k+3)=4k/(3k-1)

solve (k+1)/k=8/(k+3)

=>k^2+4k+3=8k

=>k^2–4k+3=0

=>k=1,3

Now,8/(k+3)=4k/(3k-1)

=>6k-2=k^2+3k

=>k^2–3k+2=0

=>k=1,2

Now since both the conditions must be satisfied we take the value of k which satisfies both the equation hence k=1.