# How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?

Due 02/05/2013 Please respond with at least 150 words. Thanks

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## solution of the problem

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There xx only one solution set depending on the xxxxxxxxxxxxx xxx set xxx xx xxxxxx xxxx x finite number xx solutions, or no xxxxxxxxx In xxx xxxxxx xxx xxxxxxx xx linear inequilities have xxxx one solution xxxx

xxx xxxxxxxxx

Here's a xxxxxx with no xxxxxxxxxx x < 3 and x > 5.

Here's a xxxxxx xxxx one xxxxxxxxx x <=3 xxx x >xxx

And here's x xxxxxx with xxxxxx xxxxxx xx xxxxxxxxxx x < 4and x < x

Yes,solutions xx xxxxxxx of linear xxxxxxxxxxxx xxxx to satisfy both xxxxxxxxxxxxx

example:-

Solutions to xxxxxxx xx xxxxxx xxxxxxxxxxxx may not satisfy both xxxxxxxxxxxx only when xx has xx xxxxxxxxx

xxxxxxx :-

x>0 and x<0 for nosolution

xx

x system xx xxxxxx inequalities is x set xx xxxxxx inequalities that xx deal xxxx all at xxxx in the same plane. xxxxxxx a system xx xxxxxx xxxxxxxxxxxx is xxxx two xx xxxx than xxx inequalities xxxxxxxxx

Generally a xxxxxx xx linear inequalities xxxxxxx

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## inequalities

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xxx attached xxxx with xxxxxx xxx explanations.

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xxx linear xxxxxxxxxx xxx give xxxxxxx xxxxxxxxxx

It xxx give **xxx xxxxxxxx**:

xxxxx>0

Y=x>x

x = xxxxxxxxxxxxx

This xxxxx xxx x xx xx larger xxxx xx x should be larger than zero

xx can give **xxx xxxxxxxxx**:

Y=x2 – x >x

Y=(x-3)(x+3)>x

x = (-infinity; -3) xxx xxx x xxxxxxxxx

xxxx xxxxx for Y to be larger than xx x xxxxxx be xxxxxxx x–infinity to xxx **or** xxxxxxx** **(+3, infinity)

Notice that xxx x3 xxxxxx xx solutions could xx xx for x4 could be x etc.

xxxx it xx xxxxxxxx xx have infinity solutions:

Y=sinx-0.5

xx xxx xxx xxx there xxx xxxxxxx solutions, and due xx the fact that the function is xxxxxxxxx the xxxxxx of xxxxxxxxx is infinity.

xxx about systems xx solutions:

Lets xxxx xxxxxxx at example xxx

Y=x2 – x >0

xxxxxxxxxxxx>0

x xxxx xx more xxxx xxxx if

X-3>0 xxx x+3>x

X-3<x and xxx<x

This xx x xxx of xxxxxx inequalities. xx course xx xxx xxxxxx be xxxx xxxx xxxx x+3 xx xxxx case will be xxxx xxxx than zero. In this case we xxxxxx xx xxxxxxxxx by the fact x-3>xx

xxx xxxx picture with xxx<0

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