JEE Advance - Mathematics (1980 - No. 14)
Find the solution set of the system
$$$\matrix{
{x + 2y + z = 1;} \cr
{2x - 3y - w = 2;} \cr
{x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr
} $$$
x = 1, y = 0, z = 0, w = 0
x = 0, y = 1/2, z = 0, w = -2
x = 1, y = 1, z = -2, w = -3
x = 0, y = 0, z = 1, w = -2
There is no solution that satisfies all conditions.