Question

How do you graph the system of linear inequalities `4x>y` and `x<=12`?

Answer 1

Plot the two lines using calculated values.

Explanation:

The first one should have a dotted line along the y = 4x line, as the exact solution is not included. Shade the area below the line. The second one is just a solid line at x = 12 and shading on the left side of it.

The intersection of the two solutions is the common overlapping shaded area.

Answer 2

graph{(4x-y)(12-x)^.5>0 [-156.6, 163.4, -91.5, 68.5]}

Explanation:

Draw the line `4x-y=0` passing for `(0;0)` and `(1;4)`.
Take a random easy point such as `P=(1;0)` that is to the "right" halfplane respect to the line; this point satisfy the inaquality `4x>y` because (`4>0`), so the "right" halfplane is the desired one.
The take only the zone with `x` less than 12.