Chapter 6.8, Problem 1CYU

To determine

To calculate:

Given system of inequality:

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

Answer to Problem 1CYU

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

  

Explanation of Solution

Given information:

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

Calculation:

Graph for the given inequality is as below:

  

Given system of inequality is,

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

The graph of $x\ge 4$ and $y\ge x-3$ 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 $2x+y\ge 2$ and $2x+y\le 4$ .

Because at the time of graphing more than one region, it is helpful to use two different coloured and two different patterns for each region. So, it will easy to determine the regions intersect and find possible solutions.

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 $\left(4,1\right)$ .