Graph, inequalities

Question

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

Answer 1

?Hello Kamran,

 

Sorry, but the correct answer is C.  Yes, the point (1, -1/2) is in the 4th quadrant, but it doesn't satisfy either inequality. When you plug in "1" for the "x" in the equation, y >= 2x + 1, you get the value, 3, which is not less than the y value of -1/2.

I would show the graph of the equations, but this forum does not have the upload capacity. So, graph the inequalities as if they are regular linear equations and you'll see that none of the ordered pairs in the fourth quadrant satisfies either of the inequalities.

 

I hope this helps!

John B.