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Chapter 11: Q. 54 (page 783)

In Problems 53鈥�56, write a system of linear inequalities for the given graph.

54.

Short Answer

Expert verified

The inequalities are

x鈮�0y鈮�0x鈮�6y鈮�5x+y鈮�2

Step by step solution

01

Step 1. Given information

The graph is in first quadrant so the values arex鈮�0&y鈮�0

02

Step 2. About parallel lines

The lines parallel to y-axis has equation x=k

here k=6then the equation is x=6

the lines parallel to x-axis has equation y=k

here k=5 then the equation is y=5

Due to origin not included in the region so the inequalities arex鈮�6&y鈮�5

03

Step 3. About line equation of given points

Given the points are (0,2)&(2,0)

slope:m=(y2-y1(x2-x1)

m=(2-0)(0-2)m=-1

The line equation is:

y-y1=m(x-x1)y-0=-1(x-2)y=-x+2x+y=2

The line excludes the origin so the inequality x+y鈮�2.

04

Atep 4. Solution

The inequalities bounded by the given graph

x鈮�0y鈮�0x鈮�6y鈮�5x+y鈮�2

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Most popular questions from this chapter

Graph the equation:y2=x2-1

Verify that the values of the variables listed are solutions of the system of equations.

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The product of two numbers is 10, and the difference of their squares is 21. Find the numbers.

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