Chapter 6.8, Problem 1BCYP

To determine

To calculate:

Given system of inequality:

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

Answer to Problem 1BCYP

Given inequality has no solution.

Explanation of Solution

Given information:

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

Calculation:

Graph for the given inequality is as below:

  

Given system of inequality is,

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

The graph of $2x+y\le 4$ is dashed and it is not included in the graph of the solution. The graph of $2x+y\ge 2$ is solid and it is included in 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 colouredand two different patterns for each region. So it will easy to determine the regions intersect and find possible solutions.

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 $2x+y\le 4$ the region is shaded.

Here in this both lines ae parallel so there is no solution for the given equation.