Determine whether or not the ordered pair is a solution to the equation $\newline$ $y=3 x+8$ $\newline$ (a) $(-5,-7)$ $\newline$ (b) $(-1,3)$ $\newline$ (c) $\left(\frac{1}{3}, g\right)$

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. Determine whether or not the ordered pair is a solution to the equation

\newline

y=3 x+8

\newline

(a)

(-5,-7)

\newline

(b)

(-1,3)

\newline

(c)

\left(\frac{1}{3}, g\right)

Given Equation: We are given the equation $y=3x+8$ and we need to check if the ordered pairs $(-5,-7)$ , $(-1,3)$ , and $(\frac{1}{3},g)$ are solutions to this equation. We will substitute the $x$ -value from each ordered pair into the equation and check if the corresponding $y$ -value satisfies the equation.
Ordered Pair $(-5,-7)$ : For the ordered pair $(-5,-7)$ , substitute $x = -5$ into the equation $y=3x+8$ . $\newline$ $y = 3*(-5) + 8$ $\newline$ $y = -15 + 8$ $\newline$ $y = -7$ $\newline$ Check if this is equal to the $y$ -value from the ordered pair. $\newline$ $-7 = -7$ $\newline$ Since the values match, $(-5,-7)$ is a solution to the equation.
Ordered Pair $(-1,3)$ : For the ordered pair $(-1,3)$ , substitute $x = -1$ into the equation $y=3x+8$ . $\newline$ $y = 3*(-1) + 8$ $\newline$ $y = -3 + 8$ $\newline$ $y = 5$ $\newline$ Check if this is equal to the $y$ -value from the ordered pair. $\newline$ $5 \neq 3$ $\newline$ Since the values do not match, $(-1,3)$ is not a solution to the equation.
Ordered Pair $\left(\frac{1}{3},g\right)$ : For the ordered pair $\left(\frac{1}{3},g\right)$ , substitute $x = \frac{1}{3}$ into the equation $y=3x+8$ . $\newline$ $y = 3\left(\frac{1}{3}\right) + 8$ $\newline$ $y = 1 + 8$ $\newline$ $y = 9$ $\newline$ Check if this is equal to the $y$ -value from the ordered pair. $\newline$ Since we do not have a specific value for $g$ , we cannot determine if $\left(\frac{1}{3},g\right)$ is a solution unless $\left(\frac{1}{3},g\right)$ $0$ .