Question

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

Answer 1

The lines meet at (3, 0) and the y-intercepts are `3/2 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<3/2-x/2 and y>2/3x-2`.

Now, the line `y=3/2-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,

`2/3x-2 < y < 3/2-x/2`.

Separately, this is the given pair of inequalities.

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