Chapter 6.8, Problem 1CCYP

To determine

To calculate:

Given system of inequality:

  $\begin{array}{l}y\ge -4\\ 3x+y\le 2\end{array}$

Answer to Problem 1CCYP

Solution of the function will be area under shaded region shown by graph:

  

Explanation of Solution

Given information:

  $\begin{array}{l}y\ge -4\\ 3x+y\le 2\end{array}$

Calculation:

Graph for the given inequality is as below:

  

Given system of inequality is,

  $\begin{array}{l}y\ge -4\\ 3x+y\le 2\end{array}$

Isolate $y$ for $3x+y\le 2$ ,

Subtract $3x$ from both sides so equation will be,

  $\begin{array}{l}3x+y-3x\le 2-3x\\ =\left[\begin{array}{l}y\ge -4\\ y\le 2-3x\end{array}\right]\end{array}$

Here in this equation graph of the both inequalities overlap each other.

So the solution to the system will be the area where the shadings from each inequality overlap one another.

The solution of the system is the set of ordered pairs in the intersection of the graphs of $2x+y\ge 2$ and $2x+y\le 4$ a the region is shaded.

Here in given inequalities both lines are overlap each other, so solution of the function will be area under shaded region.