Question

1. which of the following is not a solution to the system of inequalities?

options: (1, 0), (2, 0), (4, -1), (2, -2)

Explanation:

Step1: Identify inequalities from graph

First, the dashed horizontal line is $y=-2$, shaded above, so $y > -2$. The dashed sloped line passes through $(0,3)$ and $(1,-2)$, its slope is $\frac{-2-3}{1-0}=-5$, so equation is $y=-5x+3$, shaded to the right, so $y > -5x+3$.

Step2: Test point (1,0)

Substitute $x=1,y=0$:
$0 > -2$ (true); $0 > -5(1)+3=-2$ (true).

Step3: Test point (2,0)

Substitute $x=2,y=0$:
$0 > -2$ (true); $0 > -5(2)+3=-7$ (true).

Step4: Test point (4,-1)

Substitute $x=4,y=-1$:
$-1 > -2$ (true); $-1 > -5(4)+3=-17$ (true).

Step5: Test point (2,-2)

Substitute $x=2,y=-2$:
$-2 > -2$ (false, since it is not greater than); $-2 > -5(2)+3=-7$ (true). One condition fails.

Answer:

D. (2,-2)