Chapter 9.7, Problem 33PPS

To determine

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

Answer to Problem 33PPS

The common region and the intersection of the graphs of the Figure 2 shows the solution of the inequalities.

Explanation of Solution

Given:

The given system of equation is,

  $\begin{array}{l}16{\left(x-3\right)}^2+4y^2\le 64\\ y\le -\left|x-2\right|+2\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}16{\left(x-3\right)}^2+4y^2\le 64\\ y\le -\left|x-2\right|+2\end{array}$

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

  

Figure 1

The inequality $16{\left(x-3\right)}^2+4y^2\le 64$ has the sign of less than and equal to. Thus, the region tha is inside the ellipse and on the boundary of the ellipse satisfies the inequality.

The inequality $y\le -\left|x-2\right|+2$ has the sign of less than and equal to. The point $\left(2,0\right)$ that is from the interior of the graph, satisfies the inequality. Thus, the region that is interior of the graph and on the graph satisfy the inequality.

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

  

Figure 2

The common region and the intersection of the graphs represents the solution of the inequalities.