[" 15."x+(k+1)y=4],[(k+1)x+9y=5k+2],[" 16."kx+3y=2k+1]

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

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

{:(2x + (k - 2)y = k),(6x + (2k - 1) y = 2k + 5):}

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

Find the values of k for which the following pair of linear equations has infinitely many solutions : 2x - 3y = 7, ( k + 1 ) x + ( 1 - 2k) y = ( 5k - 4) .

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)}

If the angles made by the normal of the plane 2x + 3y - 4z - 16=0 with the coordinates axes X, Y, Z are Cos ^(-1) k _(1), Cos ^(-1) k _(2), Cos^(-1) k _(3), then k _(1), k _(2), k _(3) respectively are

Find the value of k for which following system of equations have infinitely many solution: x+(k+1)y=4,\ \ \ \ (k+1)x+9y=5k+2