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Solve the system of equations by substitution. $\newline$ $-3x - y - 2z = 14$ $\newline$ $-x - 2y + 2z = 6$ $\newline$ $z = -2$

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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

-3x - y - 2z = 14

\newline

-x - 2y + 2z = 6

\newline

z = -2

Substitute $z = -2$ : First, let's substitute $z = -2$ into the other two equations. $\newline$ $-3x - y - 2(-2) = 14$ $\newline$ $-x - 2y + 2(-2) = 6$
Simplify the equations: Now, simplify the equations. $\newline$ $-3x - y + 4 = 14$ $\newline$ $-x - 2y - 4 = 6$
Solve for y: Next, solve for y in terms of x from the first equation. $\newline$ $-3x - y = 14 - 4$ $\newline$ $-3x - y = 10$ $\newline$ $y = -3x - 10$
Substitute $y = -3x - 10$ : Substitute $y = -3x - 10$ into the second equation. $-x - 2(-3x - 10) - 4 = 6$
Simplify the second equation: Simplify the second equation. $-x + 6x + 20 - 4 = 6$ $5x + 16 = 6$
Solve for x: Solve for x. $\newline$ $5x = 6 - 16$ $\newline$ $5x = -10$ $\newline$ $x = -10 / 5$ $\newline$ $x = -2$
Substitute $x = -2$ : Now, substitute $x = -2$ back into $y = -3x - 10$ to find $y$ . $\newline$ $y = -3(-2) - 10$ $\newline$ $y = 6 - 10$ $\newline$ $y = -4$

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