# How do you graph the inequality x + 2y < 3, 2x – 3y<6?

Jul 3, 2016

The lines meet at (3, 0) and the y-intercepts are $\frac{3}{2} \mathmr{and} - 2$.
Shade the region on the left of (3, 0), in-between the lines. For any point (x, y) here, both the inequalities are satisfied.

#### Explanation:

Rearrange to the forms $y < \frac{3}{2} - \frac{x}{2} \mathmr{and} y > \frac{2}{3} x - 2$.

Now, the line $y = \frac{3}{2} - \frac{x}{2}$ cuts the axes at (3, 0) and (0, 3/2) and the

line #y+2/3x-2 cuts the axes at (3, 0) and (0, -2). (3, 9) is the common

point. For any point (x, y) in the region enclosed by these lines, on

the left of the common point (3,

$\frac{2}{3} x - 2 < y < \frac{3}{2} - \frac{x}{2}$.

Separately, this is the given pair of inequalities.

The opposite region, on the right of (3, 0), is for the reversed inequalities.