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Chapter 11: Q. 33 (page 783)

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility:

2x+3y≥62x+3y≤0

Short Answer

Expert verified

The graph of the given system of inequality do not exist.

Step by step solution

01

Step 1. Graph of the line 2x+3y≥6

To plot the graph of 2x+3y≥6, plot the line 2x+3y=6.

Take any arbitrary point (0,0)

Since the taken point does not satisfy the inequality, therefore, the shaded region will not include this point.

02

Step 2. Graph of the inequality 2x+3y≤0

The graph of the inequality 2x+3y≤0can be drawn by graphing 2x+3y=0

Take any arbitrary point(2,0)

The given inequality does not satisfy this point.

Thus, the shaded region will not include this point.

03

Step 3. Final Graph

The intersection of both the graphs will give the final graph of the system of inequalities.

Since, there is no intersection, Hence, the graph of the given system of inequalities does not exist.

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Most popular questions from this chapter

The difference of two numbers is the same as their product, and the sum of their reciprocals is 5. Find the numbers.

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

y=4-x2;y=2x+4

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

x - y + z = -4

2x - 3y + 4z = -15

5x + y - 2z = 12

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

3x+3y+2z=4x-y-z=02y-3z=-8x=1,y=-1,z=2;1,-1,2

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

3x-y=79x-3y=21
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