Chapter 9.7, Problem 36PPS

To determine

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

Answer to Problem 36PPS

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,

  $\begin{array}{l}18y^2-3x^2\le 54\\ y\ge \left|2x\right|-6\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}18y^2-3x^2\le 54\\ y\ge \left|2x\right|-6\end{array}$

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

  

Figure 1

The inequality $18y^2-3x^2\le 54$ has the sign of less than and equal to. Thus, the point $\left(0,0\right)$ satisfy the inequality and it includes the region of the origin and the boundary of the hyperbola.

The inequality $y\ge \left|2x\right|-6$ has the sign of greater than and equal to. Thus, the point $\left(0,0\right)$ satisfy the inequality and it includes the region of the origin and the boundary of the hyperbola.

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.