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# ​ Which graph represents the solution set to the system of inequalities?

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Which graph represents the solution set to the system of inequalities?

AngelRay  Dec 17, 2017
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The line  y + 6  =  -3x  has a y-intercept at  (0, -6) . This rules out the top two graphs.

The line  y = $$\frac13$$x + 4  is graphed correctly on both of the bottom two graphs.

The inequality says that  y  <   $$\frac13$$x + 4  , so the side below the line must be shaded.

That rules out the fourth graph. (It would have been right if the inequality was  y  >  $$\frac13$$x + 4 ).

So the third option is correct.  Here's a graph of the three inequalities from desmos:

https://www.desmos.com/calculator/qel2k86ykm

hectictar  Dec 17, 2017

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