Chapter 11, Problem 23CT

To determine

To graph: Consider the graph of inequalities $\left\{\begin{array}{l}{x}^2+y^2\le 100\\ 4x-3y\ge 0\end{array}\right\}$ .

Explanation of Solution

Given information:

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

Calculation:

Consider the graph to be shaded, use a test point $\left(0,0\right)$ .

Substitute 0 for $x$ and $y$ in the first inequality of the system.

  $\begin{array}{c}{\left(0\right)}^2+{\left(0\right)}^2\le 100\\ 0<100\end{array}$

The point $\left(0,0\right)$ satisfies the inequality $x^2+y^2\le 100$ . So, we shade inside the circle

  $x^2+y^2=100$

The graph of inequality figure-(1) shows.

  

Figure-(1)

Substitute 0 for $x$ and $y$ in the second inequality of the system.

  $\begin{array}{c}4\left(0\right)-3\left(0\right)\ge 0\\ 0=0\end{array}$

The graph of point $\left(0,0\right)$ satisfies the inequality $4x-3y\ge 0$ . figure-(1) shown.

  

Figure-(1)

Graph the system of the equation using the information above in figure-(!)

  

Figure-(1)

Therefore, the intersection of the shaded regions gives the graph of the system of inequalities.