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Solve the system of equations. $\newline$ $y = 2x + 7$ $\newline$ $y = -x - 8$ $\newline$ (, )

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Solve a system of equations using substitution

Full solution

Q. Solve the system of equations.

\newline

y = 2x + 7

\newline

y = -x - 8

\newline

(____, ____)

Substitute $y$ : Step $1$ : Substitute $y$ from the first equation into the second equation. $\newline$ Since $y = 2x + 7$ and $y = -x - 8$ , set $2x + 7 = -x - 8$ . $\newline$ $2x + 7 = -x - 8$
Solve for x: Step $2$ : Solve for x. $\newline$ Add $x$ to both sides: $2x + x + 7 = -x + x - 8$ $\newline$ $3x + 7 = -8$
Isolate x: Step $3$ : Isolate x. $\newline$ Subtract $7$ from both sides: $3x + 7 - 7 = -8 - 7$ $\newline$ $3x = -15$
Divide for $x$ : Step $4$ : Divide both sides by $3$ to find $x$ . $\frac{3x}{3} = \frac{-15}{3}$ $x = -5$
Substitute for y: Step $5$ : Substitute $x = -5$ back into the first equation to find $y$ . $y = 2(-5) + 7$ $y = -10 + 7$ $y = -3$

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