Chapter 9.7, Problem 35PPS

To determine

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

Answer to Problem 35PPS

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,

  $\begin{array}{l}2y-4\ge \left|x+4\right|\\ 12-2y>x^2+12x+36\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}2y-4\ge \left|x+4\right|\\ 12-2y>x^2+12x+36\end{array}$

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

  

Figure 1

The inequality $2y-4\ge \left|x+4\right|$ has the sign of greater than and equal to, the point $\left(0,0\right)$ from the exterior of the graph does not satisfy the inequality.

The inequality $12-2y>x^2+12x+36$ has the sign of greater than. The point $\left(0,0\right)$ that is from the exterior of the parabola does not satisfy the inequality. Thus, the interior region 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.