Chapter 9.7, Problem 31PPS

To determine

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

Answer to Problem 31PPS

The common region of the Figure 2 shows the solution of the inequalities.

Explanation of Solution

Given:

The given system of equation is,

  $\begin{array}{l}y>x^2-6x+8\\ x\ge y^2-6y+8\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}y>x^2-6x+8\\ x\ge y^2-6y+8\end{array}$

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

  

Figure 1

The inequality $y>x^2-6x+8$ has the sign of greater than and the point $\left(0,0\right)$ do not satisfy the inequality so the region other than the point $\left(0,0\right)$ satisfy the inequality.

The inequality $x\ge y^2-6y+8$ has the sign of greater than and equal to. The point that is from the exterior of the parabola does not satisfy the inequality. Thus, the region interior of the parabola and on the boundary satisfy the inequality.

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

  

Figure 2

The common region represents the solution of the system.