$\begin{array}{l} y \geq-1 \\ y \leq 4 x+1 \end{array}$ $\newline$ Which of the following ordered pairs $(x, y)$ satisfies the system of inequalities? $\newline$ Choose $1$ answer: $\newline$ (A) $(-4,2)$ $\newline$ (B) $(0,4)$ $\newline$ (C) $(2,-2)$ $\newline$ (D) $(2,4)$

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Algebra 1

Is (x, y) a solution to the system of linear inequalities?

Full solution

\begin{array}{l} y \geq-1 \\ y \leq 4 x+1 \end{array}

\newline

Which of the following ordered pairs

(x, y)

satisfies the system of inequalities?

\newline

Choose

1

answer:

\newline

(A)

(-4,2)

\newline

(B)

(0,4)

\newline

(C)

(2,-2)

\newline

(D)

(2,4)

Test $(-4, 2)$ in $y \geq -1$ : Test the ordered pair (A) $(-4, 2)$ in the inequality $y \geq -1$ . Substitute $-4$ for $x$ and $2$ for $y$ in $y \geq -1$ . $2 \geq -1$ Since $2 \geq -1$ is true, $(-4, 2)$ satisfies the first inequality.
Test $(-4, 2)$ in $y \leq 4x + 1$ : Test the ordered pair (A) $(-4, 2)$ in the inequality $y \leq 4x + 1$ . Substitute $-4$ for $x$ and $2$ for $y$ in $y \leq 4x + 1$ . $2 \leq 4(-4) + 1$ $y \leq 4x + 1$ $0$ $y \leq 4x + 1$ $1$ Since $y \leq 4x + 1$ $1$ is false, $(-4, 2)$ does not satisfy the second inequality.
Test $(0, 4)$ in $y \geq -1$ : Test the ordered pair $(B) (0, 4)$ in the inequality $y \geq -1$ . Substitute $0$ for $x$ and $4$ for $y$ in $y \geq -1$ . $4 \geq -1$ Since $4 \geq -1$ is true, $(0, 4)$ satisfies the first inequality.
Test $(0, 4)$ in $y \leq 4x + 1$ : Test the ordered pair (B) $(0, 4)$ in the inequality $y \leq 4x + 1$ . Substitute $0$ for $x$ and $4$ for $y$ in $y \leq 4x + 1$ . $4 \leq 4(0) + 1$ $y \leq 4x + 1$ $0$ $y \leq 4x + 1$ $1$ Since $y \leq 4x + 1$ $1$ is false, $(0, 4)$ does not satisfy the second inequality.
Test $(2, -2)$ in $y \geq -1$ : Test the ordered pair $(C) (2, -2)$ in the inequality $y \geq -1$ . Substitute $2$ for $x$ and $-2$ for $y$ in $y \geq -1$ . $-2 \geq -1$ Since $-2 \geq -1$ is false, $(2, -2)$ does not satisfy the first inequality.
Test $(2, 4)$ in $y \geq -1$ : Test the ordered pair $(D) (2, 4)$ in the inequality $y \geq -1$ . Substitute $2$ for $x$ and $4$ for $y$ in $y \geq -1$ . $4 \geq -1$ Since $4 \geq -1$ is true, $(2, 4)$ satisfies the first inequality.
Test $(2, 4)$ in $y \leq 4x + 1$ : Test the ordered pair $(D) (2, 4)$ in the inequality $y \leq 4x + 1$ . Substitute $2$ for $x$ and $4$ for $y$ in $y \leq 4x + 1$ . $4 \leq 4(2) + 1$ $y \leq 4x + 1$ $0$ $y \leq 4x + 1$ $1$ Since $y \leq 4x + 1$ $1$ is true, $(2, 4)$ satisfies the second inequality.