Question

In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points

$51.\left\{\begin{array}{l}x\ge 0\\ y\ge 0\\ x+2y\ge 1\\ x+2y\le 10\end{array}\right.$

Short answer

The shaded region shows the bounded region

Step-by-step solution

step 1. introduction

Consider the first inequality in the system of inequalities is$x\ge 0$& $y\ge 0$

we get the shaded region

step 2.consideration of third inequality

$x+2y\ge 1$,the equation of the equality consider by replacing with equality$x+2y=1$

For determining the shaded portion we use to test a point with $(0,0)$

$$\begin{gathered} 0+0\ge 1 \\ 0\ge 1 \end{gathered}$$

The shaded part does not include the point$(0,0)$in the inequality$x+2y\ge 1$

step 3. consideration of fourth inequality

$x+2y\le 10$,the equation of line is replacing by inequality with equality $x+2y=10$

By substituting by test point $(0,0)$

$$\begin{gathered} 0+0\le 10 \\ 0\le 10 \end{gathered}$$

The point $(0,0)$does not contains the shaded portion in the equation $x+2y\le 10$

step 4. The solution 

The shaded portion is the bounded by all inequalities