Q. 36 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35–42, graph each system of inequalities by hand. 

$\left\{\begin{array}{l}{x}^2+y^2\ge 9\\ x+y\le 3\end{array}\right.$

Step-by-Step Solution

Answer

The graph is

Step 1. Graph of the inequality x 2 + y 2 ≥ 9

The graph of the inequality $x^2+y^2\ge 9$ will be a circle.

Since, the point $(0,0)$does not satisfy the inequality, it will not be included in the shaded region.

Step 2. Graph of x + y ≤ 3

First, plot the line$x+y=3$

Now, the point$(0,0)$ satisfies the inequality $x+y\le 3$,

therefore, it will be included in the shaded region.

Step 3. Final graph

The final graph will be the intersection of the two graphs,