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{:[y < 3x+4],[y < 5x+2]:}
Which of the following ordered pairs
(x,y) satisfies the system of inequalities?
Choose 1 answer:
(A)
(-1,0)
(B)
(1,7)
(c)
(2,11)
(D)
(3,-4)

$\begin{array}{l} y<3 x+4 \\ y<5 x+2 \end{array}$ $\newline$ Which of the following ordered pairs $(x, y)$ satisfies the system of inequalities? $\newline$ Choose $1$ answer: $\newline$ (A) $(-1,0)$ $\newline$ (B) $(1,7)$ $\newline$ (C) $(2,11)$ $\newline$ (D) $(3,-4)$

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

Full solution

Q.

\begin{array}{l} y<3 x+4 \\ y<5 x+2 \end{array}

\newline

Which of the following ordered pairs

(x, y)

satisfies the system of inequalities?

\newline

Choose

1

answer:

\newline

(A)

(-1,0)

\newline

(B)

(1,7)

\newline

(C)

(2,11)

\newline

(D)

(3,-4)

Test $(-1,0)$ in $1$ st inequality: Test the ordered pair (A) $(-1,0)$ in the first inequality y < 3x+4. Substitute $-1$ for $x$ and $0$ for $y$ . 0 < 3(-1) + 4 0 < -3 + 4 0 < 1 Since 0 < 1 is true, $(-1,0)$ satisfies the first inequality y < 3x+4.
Test $(-1,0)$ in $2$ nd inequality: Test the ordered pair $A$ $(-1,0)$ in the second inequality y < 5x+2. $\newline$ Substitute $-1$ for $x$ and $0$ for $y$ . $\newline$ 0 < 5(-1) + 2 $\newline$ 0 < -5 + 2 $\newline$ $A$ $0$ $\newline$ Since $A$ $0$ is false, $(-1,0)$ does not satisfy the second inequality y < 5x+2.
Test $1,7$ in $1$ st inequality: Test the ordered pair (B) $1,7$ in the first inequality y < 3x+4. Substitute $1$ for $x$ and $7$ for $y$ . 7 < 3(1) + 4 7 < 3 + 4 7 < 7 Since 7 < 7 is false ( $7$ is not less than $7$ , they are equal), $1,7$ does not satisfy the first inequality y < 3x+4.
Test $2,11$ in $1$ st inequality: Test the ordered pair (C) $2,11$ in the first inequality y < 3x+4. Substitute $2$ for $x$ and $11$ for $y$ . 11 < 3(2) + 4 11 < 6 + 4 11 < 10 Since 11 < 10 is false, $2,11$ does not satisfy the first inequality y < 3x+4.
Test $3,-4$ in $1$ st inequality: Test the ordered pair $D$ $3,-4$ in the first inequality y < 3x+4. $\newline$ Substitute $3$ for $x$ and $-4$ for $y$ . $\newline$ -4 < 3(3) + 4 $\newline$ -4 < 9 + 4 $\newline$ -4 < 13 $\newline$ Since \\(-4\) < \(13\)\$ is true, $3,-4$ satisfies the first inequality y < 3x+4.
Test $3,-4$ in $2$ nd inequality: Test the ordered pair (D) $3,-4$ in the second inequality y < 5x+2. Substitute $3$ for $x$ and \\ $-4$ \) for $y$ . (-4\) < $5$ ( $3$ ) + $2$ \ (-4\) < $15$ + $2$ \ (-4\) < $17$ \ Since (-4\) < $17$ \ is true, $3,-4$ satisfies the second inequality y < 5x+2.

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