MHB Which Quadrant Contains No Solutions to This System of Inequalities?

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The system of inequalities y ≥ 2x + 1 and y > x/2 - 1 is analyzed to determine which quadrant contains no solutions. The discussion reveals that quadrants I, II, and III contain solutions, while quadrant IV does not. There is confusion regarding the correct answer, with some participants believing there are solutions in all quadrants. However, the consensus is that quadrant IV is indeed the one without solutions. The final conclusion confirms that quadrant IV is the correct answer.
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If the system of inequalities y ≥ 2x + 1 and y> x/2-1
is graphed in the xy-plane above, which
quadrant contains no solutions to the system?
A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants.


I thing the answer is D . But book says that it is C. I think C is wrong 'cause from the second inequality we can get (1;-1/2) or (2;-1) which are in 4 quadrant
 
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?? No, they are not! -\frac{1}{2} is NOT larger than 2\left(-\frac{1}{2}\right)+ 1= 0. And -1 is NOT larger than 2\left(2\right)+ 1= 5.<br /> <br /> Is it possible that you are thinking &quot;(y, x)&quot; rather than &quot;(x, y)&quot;?
 
kamranpiriyev said:
If the system of inequalities y ≥ 2x + 1 and y> x/2-1
is graphed in the xy-plane above, which
quadrant contains no solutions to the system?
A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants.


I thing the answer is D . But book says that it is C. I think C is wrong 'cause from the second inequality we can get (1;-1/2) or (2;-1) which are in 4 quadrant

Let's graph the system of inequalities:

[desmos="-10,10,-10,10"]y\ge2x+1;y\gt x/2-1[/desmos]

From this we can see quadrants I-III contain solutions, and quadrant IV has no solutions. :)
 
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