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

Sep 5, 2017

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.

Sep 5, 2017

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

#### Explanation:

Draw the line $4 x - y = 0$ 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 $4 x > y$ because ($4 > 0$), so the "right" halfplane is the desired one.
The take only the zone with $x$ less than 12.