$\begin{cases} y \geq -1 \\ y \leq 4x+1 \end{cases}$ $\newline$ 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?

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

\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 $(-4, 2)$ : Let's test each ordered pair to see if it satisfies both inequalities. $\newline$ First, we'll test option (A) $(-4, 2)$ . $\newline$ For the inequality $y \geq -1$ , substitute $x = -4$ and $y = 2$ : $\newline$ $2 \geq -1$ $\newline$ This is true, so $(-4, 2)$ satisfies the first inequality.
Eliminate option (A): Now, let's test $(-4, 2)$ in the second inequality $y \leq 4x + 1$ : $\newline$ $2 \leq 4(-4) + 1$ $\newline$ $2 \leq -16 + 1$ $\newline$ $2 \leq -15$ $\newline$ This is false, so $(-4, 2)$ does not satisfy the second inequality. $\newline$ Since it does not satisfy both inequalities, we can eliminate option (A).
Test $0, 4$ : Next, we'll test option (B) $0, 4$ . For the inequality $y \geq -1$ , substitute $x = 0$ and $y = 4$ : $$4 \geq $-1$ \$) This is true, so \(0, 4$ satisfies the first inequality.
Eliminate option (B): Now, let's test $(0, 4)$ in the second inequality $y \leq 4x + 1$:\[4 \leq 4(0) + 1\]\[4 \leq 0 + 1\]\[4 \leq 1\]This is false, so $(0, 4)$ does not satisfy the second inequality. Since it does not satisfy both inequalities, we can eliminate option (B).
Test $ (2, -2):$ Next, we'll test option (C) $ (2, -2)$. For the inequality $ y \geq -1$, substitute $ x = 2 $ and $ y = -2$: $ -2 \geq -1$ This is false, so $ (2, -2)$ does not satisfy the first inequality. Since it does not satisfy the first inequality, we can eliminate option (C) without testing the second inequality.
Eliminate option (C): Finally, we'll test option (D) $(2, 4)$. For the inequality $y \geq -1$, substitute $x = 2$ and $y = 4$: $4 \geq -1$ This is true, so $(2, 4)$ satisfies the first inequality.
Test $2, 4$: Now, let's test $2, 4$ in the second inequality $y \leq 4x + 1$:\[4 \leq 4(2) + 1\]\[4 \leq 8 + 1\]\[4 \leq 9\]This is true, so $2, 4$ satisfies the second inequality.\Since $2, 4$ satisfies both inequalities, it is the solution to the system of inequalities.