Solve using substitution. –6x − 2y = –8 y = 7 (_____, _____)

Identify Variable Equation: Identify the equation that is already solved for one variable. The second equation is already solved for y: y = 7.Substitute Value of y: Substitute the value of y into the first equation. The first equation is –6x − 2y = –8. Since y = 7, we substitute 7 in place of y to get –6x − 2(7) = –8.Simplify and Solve for x: Simplify the equation and solve for x. –6x − 2(7) = –8 simplifies to –6x − 14 = –8. Now, we add 14 to both sides to isolate the term with x: –6x = –8 + 14.Continue Solving for x: Continue solving for x. –6x = 6. Now, we divide both sides by –6 to find x: x = 6 / (–6).Calculate x Value: Calculate the value of x. x = 6 / (–6) gives us x = –1.Write Solution as Ordered Pair: Write the solution as an ordered pair. Since y = 7 and x = –1, the solution to the system of equations is (–1, 7).

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Solve using substitution. $\newline$ $-6x - 2y = -8$ $\newline$ $y = 7$ $\newline$ (_, _)

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Precalculus

Solve a system of equations using substitution

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Q. Solve using substitution.

\newline

-6x - 2y = -8

\newline

y = 7

\newline

(_____, _____)

Identify Variable Equation: Identify the equation that is already solved for one variable. $\newline$ The second equation is already solved for $y$ : $y = 7$ .
Substitute Value of $y$ : Substitute the value of $y$ into the first equation. $\newline$ The first equation is $–6x − 2y = –8$ . Since $y = 7$ , we substitute $7$ in place of $y$ to get $–6x − 2(7) = –8$ .
Simplify and Solve for x: Simplify the equation and solve for $x$ . $–6x − 2(7) = –8$ simplifies to $–6x − 14 = –8$ . Now, we add $14$ to both sides to isolate the term with $x$ : $–6x = –8 + 14$ .
Continue Solving for x: Continue solving for x. $-6x = 6$ . Now, we divide both sides by $-6$ to find $x$ : $x = \frac{6}{(-6)}$ .
Calculate x Value: Calculate the value of x. $\newline$ $x = \frac{6}{(\text{–}6)}$ gives us $x = \text{–}1$ .
Write Solution as Ordered Pair: Write the solution as an ordered pair. $\newline$ Since $y = 7$ and $x = -1$ , the solution to the system of equations is $(-1, 7)$ .