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Chapter 11: Q. 51 (page 783)

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

51.x鈮�0y鈮�0x+2y鈮�1x+2y鈮�10

Short Answer

Expert verified

The shaded region shows the bounded region

Step by step solution

01

step 1. introduction

Consider the first inequality in the system of inequalities isx鈮�0& y鈮�0

we get the shaded region

02

step 2.consideration of third inequality

x+2y鈮�1,the equation of the equality consider by replacing with equalityx+2y=1

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

0+0鈮�10鈮�1

The shaded part does not include the point(0,0)in the inequalityx+2y鈮�1

03

step 3. consideration of fourth inequality

x+2y鈮�10,the equation of line is replacing by inequality with equality x+2y=10

By substituting by test point (0,0)

0+0鈮�100鈮�10

The point (0,0)does not contains the shaded portion in the equation x+2y鈮�10

04

step 4. The solution 

The shaded portion is the bounded by all inequalities

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Most popular questions from this chapter

Solve each system of equations. If the system has no solution, say that it is inconsistent.

5x-y=212x+3y=-12

The ratio of a to b is23. The sum of a and b is 10. What is the ratio of a+b to b-a?

Graph each inequality by hand.

y鈮�x2-1

Solve each system of equations. If the system has no solution, say that it is inconsistent.

x-y-z=12x+3y+z=23x+2y=0

Graph the equation:x2+4y2=4
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