SOLUTION: Find the solution of the system of inequalities <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/11.png" alt="Photobucket

SOLUTION: Find the solution of the system of inequalities <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/11.png" alt="Photobucket - Video and Image Hosting">

Question 172799: Find the solution of the system of inequalities

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Graphing Inequality #1
Graphing Inequality #2
Graphing Inequality #3
Graphing all three inequalities together
Solution

Inequality #1

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Start with the 1st inequality.

Subtract from both sides.

Divide both sides by to isolate .

Break up the fraction.

Reduce

Rearrange the terms.

So in order to graph , we need to graph the equation

Graph

Now since the inequality sign of is a "greater-than or equal to" sign, this tells us to shade the region above the graph (since points in that region have larger y values)

So the shading looks like this:

Graph of with the shaded region in green

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Inequality #2

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Start with the 2nd inequality.

Subtract from both sides.

Rearrange the terms.

So in order to graph , we need to graph the equation

Graph

Now since the inequality sign of is a "less-than" sign, this tells us to shade the region below the graph (since points in that region have smaller y values)

So the shading looks like this:

Graph of with the shaded region in green

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Inequality #3

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Finally, to graph , we need to graph (which is a horizontal line at y=3) like this

Graph

Now shade the region above the line (since the sign is a "greater-than" sign) to get

Graph of with the shaded region in green

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Graphing the inequalities together on the same coordinate systems

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Now simply graph the inequalities together. To do this, simply graph each line together and their corresponding region to get (note: use different colors to represent the shaded regions)

Here is a cleaner look at the intersection of regions

Here is the intersection of the 3 regions represented by the series of dots

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Solution:

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So the solution of the system of inequalities is

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