Chapter 13.4, Problem 4PSB

To determine

To find: The intersection of the solution sets of the two inequalities by the graph.

Answer to Problem 4PSB

The intersection of the solution sets of the two inequalities by the graph is shown below.

Explanation of Solution

Given:

The given inequalities are:

  $\begin{array}{c}y>2\\ x+2y<6\end{array}$

Graph is described as:

Boundary has the equation

  $\begin{array}{c}y=2\&\\ x+2y=6\end{array}$

The shaded region is defined as:

  $\begin{array}{c}0>2\left[\text{false}\right]\\ 0+2\left(0\right)<6\left[\text{true}\right]\end{array}$

The graph is shaded below the graph line $x+2y=6$ and above the graph line $y=2$ .

The graph is given as:

  

Therefore the intersection of the solution sets of the two inequalities by the graph is shown above.