Chapter 13, Problem 34RP

To determine

To find: The number of lattice points in the intersection of the system.

Answer to Problem 34RP

The number of lattice points are 66.

Explanation of Solution

Given:

The given equation is,

  $\begin{array}{l}x>0\\ y>0\\ y<-\left|x-4\right|+10\end{array}$

Calculation:

Consider the given equation is,

  $\begin{array}{l}x>0\\ y>0\\ y<-\left|x-4\right|+10\end{array}$

The graph for the intersection of the given equations is shown in Figure 1

  

Figure 1

From the above graph, the lattice points are 66 in total.