x + 2y le 10, x + y ge 1, x - y le 0, x ge 0, y ge 0

1.	x + 2y le 10, x + y ge 1, x - y le 0, x ge 0, y ge 0
Answer» Solution :First inequation : `x + 2y le 10` Corresponding equation :`x + 2y = 10` This line PASSES through the points A(10, 0) and B(0, 5). Join AB. At POINT (0, 0) , from the inequation, 0le10 (True) `:.`The Solution of this inequation is that region of XY-plane divided by line AB in which (0, 0) lie. Second inequation : ` x + y ge 1` Corresponding equation: `x + y =1` This line passes through the points C(1, 0) and D(0, 1).join CD. At point (0, 0), From the inequation, `0 ge 1` (FALSE) `:.` The solution of this inequation is that region of XY-plane divided by line AB in which (0, 0) lie. Third inequation : `x- y le0` Corresponding inequation : `x - y = 0` This line passes through the points O(0, 0) and E(2, 2) . Join OE. At point (1, 0 ), from the inequation, `1 ge 0` (False) `:,` The solution of this inequation is that region of XY-plane divided by line OE in which (1, 0) does not lie. The solution of x`ge` 0, y `ge` 0 is in first quadrant `:.` The solution of GIVEN inequation is shown by the shaded region.

Discussion