Question

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

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

Short answer

The graph is

Step-by-step solution

Step 1. Graph of the inequality x2+y2≥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,