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y < -4x+4
Which point (x,y) is a solution to the given inequality in the xy-plane?
A) (2,-1)
B) (2,1)
C) (0,5)
D) (-4,0)

y<-4 x+4 $\newline$ Which point $(x, y)$ is a solution to the given inequality in the $x y$ -plane? $\newline$ A) $(2,-1)$ $\newline$ B) $(2,1)$ $\newline$ C) $(0,5)$ $\newline$ D) $(-4,0)$

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Solve quadratic inequalities

Full solution

Q.

y<-4 x+4

\newline

Which point

(x, y)

is a solution to the given inequality in the

x y

-plane?

\newline

A)

(2,-1)

\newline

B)

(2,1)

\newline

C)

(0,5)

\newline

D)

(-4,0)

Understand the inequality: Understand the inequality. $\newline$ The inequality y < -4x + 4 represents a region in the $xy$ -plane below the line $y = -4x + 4$ . We need to find which of the given points lies in this region.
Test point A $(2, -1)$ : Test point A $(2, -1)$ . $\newline$ Substitute $x = 2$ and $y = -1$ into the inequality to check if it holds true. $\newline$ -1 < -4(2) + 4 $\newline$ -1 < -8 + 4 $\newline$ -1 < -4 $\newline$ This is true, so point A $(2, -1)$ is a solution to the inequality.
Test point B $2, 1$ : Test point B $2, 1$ . $\newline$ Substitute $x = 2$ and $y = 1$ into the inequality to check if it holds true. $\newline$ 1 < -4(2) + 4 $\newline$ 1 < -8 + 4 $\newline$ 1 < -4 $\newline$ This is false, so point B $2, 1$ is not a solution to the inequality.
Test point C $(0, 5)$ : Test point C $(0, 5)$ . $\newline$ Substitute $x = 0$ and $y = 5$ into the inequality to check if it holds true. $\newline$ 5 < -4(0) + 4 $\newline$ 5 < 0 + 4 $\newline$ 5 < 4 $\newline$ This is false, so point C $(0, 5)$ is not a solution to the inequality.
Test point D $(-4, 0)$ : Test point D $(-4, 0)$ . $\newline$ Substitute $x = -4$ and $y = 0$ into the inequality to check if it holds true. $\newline$ 0 < -4(-4) + 4 $\newline$ 0 < 16 + 4 $\newline$ 0 < 20 $\newline$ This is true, so point D $(-4, 0)$ is a solution to the inequality.

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