Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

Graph the system of inequalities: 

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

Step-by-Step Solution

Answer

The final graph is 

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 x and y in 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 x and y ,

So the graph of inequality is

Step 4. Final graph

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