Question

Find the graphical solution of the following system of linear inequations:
${\displaystyle \frac{\text{x}}{60}+\frac{\text{y}}{90}\le 1}$, ${\displaystyle \frac{\text{x}}{120}+\frac{\text{y}}{75}\le 1}$, y ≥ 0, x ≥ 0

Answer 1

Consider the equations:
${\displaystyle \frac{\text{x}}{60}+\frac{\text{y}}{90}\le 1}$

x	60	0
y	0	90

The two points on the axes are (60, 0) and (0, 90) as in equation 60 and 90 are x and y-intercepts,
(x and y are equivalent to X and Y axes.)
∵ The inequation ${\displaystyle \frac{\text{x}}{60}+\frac{\text{y}}{90}\le 1}$ satisfies the origin.
The solution set is towards the origin.
${\displaystyle \frac{\text{x}}{120}+\frac{\text{y}}{75}\le 1}$ 

x	120	0
y	0	75

The two points on the axes are (120, 0) and (0, 75) respectively.
The inequation ${\displaystyle \frac{\text{x}}{120}+\frac{\text{y}}{75}\le 1}$ satisfies the origin.

The solution set of the inequation is towards origin x ≥ 0, y ≥0 are the inequations showing the conditions that the solutions set (common region) is in the first quadrant