# Chapter 7 - Review Exercises - Page 878: 47

The graph is shown below:

#### Work Step by Step

Let us consider the inequalities \begin{align} & 2x-y\ge 4 \\ & x+2y<2 \\ \end{align} Substitute the equals symbol in place of the inequality and rewrite the equation as given below: \begin{align} & 2x-y=4 \\ & x+2y=2 \\ \end{align} To find the value of the x-intercept, substitute y = 0 as given below: \begin{align} & 2x-y=4 \\ & 2x-0=4 \\ & x=2 \end{align} Therefore, the coordinates of the line are $\left( 2,0 \right)$. To find the value of the y-intercept, substitute x = 0 as given below: \begin{align} & 2x-y=4 \\ & \left( 2\times 0 \right)-y=4 \\ & y=-4 \end{align} Therefore, the coordinates of the line are $\left( 0,-4 \right)$. Consider the second equation: $x+2y=2$, To find the value of the x-intercept, substitute y = 0 as given below: \begin{align} & x+2y=2 \\ & x+\left( 2\times 0 \right)=2 \\ & x=2 \end{align} Thus, the coordinates of the line are $\left( 2,0 \right)$. To find the value of the y-intercept, substitute x = 0 as given below: \begin{align} & x+2y=2 \\ & 0+2y=2 \\ & y=1 \end{align} Therefore, the coordinates of the line are $\left( 0,1 \right)$. Then, take origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade: $2x-y\ge 4\text{ and }x+2y<2$ $2*0-0\ge 4\text{ and }0+2*0<2$ $0\ge 4\text{ and }0<2$ So the origin is not included.

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