# How do you graph the system of inequalities x + y <=3 and x – y <=4?

Jul 24, 2018

See graph and details.

#### Explanation:

$x + y \le 3 \Rightarrow y \le 3 - x \mathmr{and} y \ge x - 4$. Combining,

$x - 4 \le y < = 3 - x \Rightarrow x \le \frac{7}{2}$.

Graph:
graph{(x+y-3)(x-y-4)(x-7/2)<=0}
The shaded region on the left ($\leftarrow$) of x = 7/2, including the

terminal junction $\left(\frac{7}{2} , - \frac{1}{2}\right)$, is the solution.

O is within. The region on the right is for reversed inequality, in

both.