Solve the system of equations by substitution. -2x + y - z = -8 -3x - 3y - 3z = -9 z = -2 ____

Solve for y: Solve for y using the first equation by substituting z = -2. -2x + y - (-2) = -8 -2x + y + 2 = -8 y = -8 - 2 + 2x y = -10 + 2xSubstitute y and z: Substitute y and z into the second equation. -3x - 3(-10 + 2x) - 3(-2) = -9 -3x + 30 - 6x + 6 = -9 Combine like terms. -9x + 36 = -9Combine like terms: Solve for x. -9x = -9 - 36 -9x = -45 x = -45 / -9 x = 5Solve for x: Substitute x back into the equation for y. y = -10 + 2(5) y = -10 + 10 y = 0Substitute x back: We already have z from the third equation. z = -2

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Solve the system of equations by substitution. $\newline$ $-2x + y - z = -8$ $\newline$ $-3x - 3y - 3z = -9$ $\newline$ $z = -2$

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Precalculus

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

-2x + y - z = -8

\newline

-3x - 3y - 3z = -9

\newline

z = -2

Solve for y: Solve for y using the first equation by substituting $z = -2$ . $\newline$ $-2x + y - (-2) = -8$ $\newline$ $-2x + y + 2 = -8$ $\newline$ $y = -8 - 2 + 2x$ $\newline$ $y = -10 + 2x$
Substitute y and z: Substitute y and z into the second equation. $\newline$ $-3x - 3(-10 + 2x) - 3(-2) = -9$ $\newline$ $-3x + 30 - 6x + 6 = -9$ $\newline$ Combine like terms. $\newline$ $-9x + 36 = -9$
Combine like terms: Solve for $x$ . $-9x = -9 - 36$ $-9x = -45$ $x = \frac{-45}{-9}$ $x = 5$
Solve for $x$ : Substitute $x$ back into the equation for $y$ . $y = -10 + 2(5)$ $y = -10 + 10$ $y = 0$
Substitute $x$ back: We already have $z$ from the third equation. $z = -2$