Chapter 6.8, Problem 1DCYP

To determine

To calculate:

Given system of inequality:

  $\begin{array}{l}x+y>2\\ -4x+2y<8\end{array}$

Answer to Problem 1DCYP

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

  

Explanation of Solution

Given information:

  $\begin{array}{l}x+y>2\\ -4x+2y<8\end{array}$

Calculation:

Graph for the given inequality is as below:

  

Given system of inequality is,

  $\begin{array}{l}x+y>2\\ -4x+2y<8\end{array}$

Initially, isolate $y$ for $x+y>2$

Subtract $x$ from both sides

  $\begin{array}{l}x+y-x>2-x\\ =y>2-x\end{array}$

Then isolate $y$ for $-4x+2y<8$ :

Add $4x$ to both sides

  $\begin{array}{l}-4x+2y+4x<8+4x\\ =2y<8+4x\end{array}$

After simplifying,

  $y<2\left(x+2\right)$

The graph of $x+y>2$ and $-4x+2y<8$ is included in the graph of the solution.

The solution of system is the set of ordered pairs in intersection of the graphs of graphs of $x+y>2$ and $-4x+2y<8$ .

This intersection point of two lines is nothing but the solution set of given system of equation.

Therefore, one solution of given system of equation is labelled as $\left(-0.667,2.667\right)$ .