Question

question number 27 in the picture

Answer 1

$x - y = 2 - - - (1) \\ kx + y = 3 - - - (2) \\ (1) + (2) \: gives \\ x = \frac{5}{1 + k} \\ substituting \: \: in \: \: (1) \\ y = x - 2 = \frac{3 - 2k}{1 + k} \\ \\ since \: x \: \: and \: \: y \: \: are \: \: in \: \: first \\ quadrant \: \: x > 0 \: \: and \: \: y > 0 \\ \\ x > 0 \: \: means \: 1 + k > 0 \\ so \: \: k > - 1 - - - (3)\\ y > 0 \: \: means \: 3 - 2k > 0 \\ so \: k < \frac{3}{2} - - - (4) \\ \\ from \: (3) \: \: and \: \: (4) \: \: option \: (D)$

Answer 2

Answer:

c) is answer dear friend