Question

Graph the system of inequalities:

$\left\{\begin{array}{l}{x}^2+y^2\le 100\\ 4x-3y\ge 0\end{array}\right.$

Short answer

The final graph is

Step-by-step solution

Step 1. Given information

A system of equation is given as

$\left\{\begin{array}{l}{x}^2+y^2\le 100\\ 4x-3y\ge 0\end{array}\right.$

Step 2. Plotting graph

First draw the circle $x^2+y^2=100$,

Substitute the values of xand yin the first inequality,

$$\begin{gathered} (0{)}^2+(0{)}^2\le 100 \\ 0<100 \end{gathered}$$

Therefore the graph is

Step 3. Graph for linear inequality

Now plot the graph of inequality ,

Substitute zero for xand y ,

So the graph of inequality is

Step 4. Final graph

By combining the both graphs of inequality, the final graph is