Which Quadrant Contains No Solutions to This System of Inequalities?

[kamranpiriyev]

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

 

[HallsofIvy]

?? No, they are not! $$-\frac{1}{2}$$ is NOT larger than [tex]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 "(y, x)" rather than "(x, y)"?[/tex]

 

[MarkFL]

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. :)