Chapter 9.7, Problem 32PPS

To determine

To find: The solution for the given system of the equation.

Answer to Problem 32PPS

The common region between the two graphs of the Figure 2 shows the solution of the inequalities.

Explanation of Solution

Given:

The given system of equation is,

  $\begin{array}{l}{x}^2+y^2\ge 9\\ 25x^2+64y^2\le 1600\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}{x}^2+y^2\ge 9\\ 25x^2+64y^2\le 1600\end{array}$

The graph for the above two equation is shown in Figure 1

  

Figure 1

The inequality $x^2+y^2\ge 9$ has the sign of greater than and equal to sign, so the region that is exterior to the circle and is on the boundary of the circle satisfies the inequality.

The inequality $25x^2+64y^2\le 1600$ has the sign of less than and equal to. The point $\left(0,0\right)$ that is from the interior of the ellipse satisfies the inequality. Thus the region that is interior of the ellipse and on the boundary of the ellipse will satisfy the inequality.

Thus, the solution for the inequalities is shown in Figure 2

  

Figure 2

The common region between the two graphs represents the solution of the inequalities.