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Solve the system of equations by substitution. $\newline$ $2x - 2y - 2z = 2$ $\newline$ $x = 7$ $\newline$ $-3x + 3y + z = -9$

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Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

2x - 2y - 2z = 2

\newline

x = 7

\newline

-3x + 3y + z = -9

Substitute $x = 7$ : First, let's substitute $x = 7$ into the other two equations. $\newline$ $2(7) - 2y - 2z = 2$ $\newline$ $-3(7) + 3y + z = -9$
Simplify equations: Now, let's simplify both equations. $\newline$ $14 - 2y - 2z = 2$ $\newline$ $-21 + 3y + z = -9$
Solve for y in first equation: Next, we'll solve the first equation for y. $\newline$ $14 - 2y - 2z = 2$ $\newline$ $-2y - 2z = 2 - 14$ $\newline$ $-2y - 2z = -12$
Divide by $-2$ for $y$ : Divide the whole equation by $-2$ to solve for $y$ . $y + z = 6$
Solve for y in second equation: Now, let's solve the second equation for y. $\newline$ $-21 + 3y + z = -9$ $\newline$ $3y + z = -9 + 21$ $\newline$ $3y + z = 12$
Divide by $3$ for y: Divide the whole equation by $3$ to solve for y. $\newline$ $y + \frac{z}{3} = 4$ $\newline$ Oops, this step contains a mistake. We should not divide $z$ by $3$ when dividing the whole equation by $3$ .

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