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The system of inequalities
y >= -x-3 and
y >= 3x is graphed in the
xy-plane. Which of the following is a solution to the system?
Choose 1 answer:
(A)
(-4,-2)
B)
(-2,0)
(C)
(0,-3)
(D)
(3,4)

The system of inequalities $y \geq-x-3$ and $y \geq 3 x$ is graphed in the $x y$ -plane. Which of the following is a solution to the system? $\newline$ Choose $1$ answer: $\newline$ (A) $(-4,-2)$ $\newline$ B) $(-2,0)$ $\newline$ (C) $(0,-3)$ $\newline$ (D) $(3,4)$

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Find the focus or directrix of a parabola

Full solution

Q. The system of inequalities

y \geq-x-3

and

y \geq 3 x

is graphed in the

x y

-plane. Which of the following is a solution to the system?

\newline

Choose

1

answer:

\newline

(A)

(-4,-2)

\newline

B)

(-2,0)

\newline

(C)

(0,-3)

\newline

(D)

(3,4)

Check Option (A): We need to check which of the given options satisfies both inequalities. Let's start with option (A) $(-4,-2)$ . $\newline$ First inequality: $y \geq -x - 3$ $\newline$ Substitute $x = -4$ and $y = -2$ into the inequality: $\newline$ $-2 \geq -(-4) - 3$ $\newline$ $-2 \geq 4 - 3$ $\newline$ $-2 \geq 1$
Check Option (B): Since option (A) did not satisfy the first inequality, we do not need to check the second inequality for option (A). Let's move on to option (B) $(-2,0)$ . $\newline$ First inequality: $y \geq -x - 3$ $\newline$ Substitute $x = -2$ and $y = 0$ into the inequality: $\newline$ $0 \geq -(-2) - 3$ $\newline$ $0 \geq 2 - 3$ $\newline$ $0 \geq -1$
Check Option (C: Second inequality: $y \geq 3x$ $\newline$ Substitute $x = -2$ and $y = 0$ into the inequality: $\newline$ $0 \geq 3(-2)$ $\newline$ $0 \geq -6$

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\newline

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