# How do you graph y + x > 2, color(white)("d")y ≤ 3x - 2?

Nov 14, 2016

See explanation

#### Explanation:

First consider $y + x > 2$

Subtract $x$ from both sides giving: $\text{ } y > - x + 2$

Plot the two lines in the normal way. Remembering that because
we DO NOT HAVE $\ge$ in $y > - x + 2$ the plotted line is dotted.

$y > - x + 2 \text{ } \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
$y \le 3 x - 2 \text{ } \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(2\right)$

The shaded area is that of all of the solutions for this system.

It is the area that is at the same time above equation(1)'s line and below equation(2)'s line. The proper wording is: the intersection of the two areas.

Not that equation(1)'s line is dotted. This indicates that the values are not permitted to be $y = - x + 2$ but must always be greater than $y$