k के कितने मानो के लिए समीकरण निकाय
`(k +1) x + 8y = 4k`
`kx + (k +3) y = 3k -1`
के अनंत हल होंगे ?

( k - 1 ) x - y = 5 , (k + 1 ) x + ( 1 - k ) y = ( 3k + 1 )

{:((k - 3)x + 3y = k),(kx + ky = 12):}

5x + 2y = 2k , 2 (k + 1 ) x + ky = (3k + 4)

{:(kx + 3y = k - 3),(12x + ky = k):}

{:(2x + 3y = 2),((k + 2)x + (2k + 1)y = 2(k - 1)):}

For how many values of k. will the system of equations (k + 1) x + 8y = 4k and kx + (k + 3) y = 3k - 1 , have an infinite number of solutions

If x = 1, y = 3 and x + y = K . Find the value of K.

det [[x ^ (k), x ^ (k + 2), x ^ (k + 3) y ^ (k), y ^ (k + 2), y ^ (k + 3) z ^ (k) , z ^ (k + 2), z ^ (k + 3)]] = (xy) (yz) (zx) {(1) / (x) + (1) / (y) + (1) / ( from)}

The value of k for which the graph of (k- 1)x+ y-2= 0 and (2-k)x-3y+ 1) =0 are parallel is k का मान जिसके लिए (k- 1)x+ y-2= 0 और (2-k)x-3y+ 1) =0 के ग्राफ समांतर हो, है-