Solve the system of equations by substitution. -2x - 2y + z = 19 y = -8 -x + 3y - 3z = -19 ____

Substitute y = -8: First, let's substitute y = -8 into the other two equations. -2x - 2(-8) + z = 19 -x + 3(-8) - 3z = -19Simplify the equations: Now, simplify the equations. -2x + 16 + z = 19 -x - 24 - 3z = -19Subtract and add constants: Subtract 16 from both sides in the first equation. -2x + z = 3Solve for z: Add 24 to both sides in the second equation. -x - 3z = 5Substitute z into equation: Now, let's solve for z from the first equation. z = 3 + 2xDistribute and combine terms: Substitute z = 3 + 2x into the second equation. -x - 3(3 + 2x) = 5Combine x terms: Distribute and combine like terms. -x - 9 - 6x = 5Add to isolate x: Combine -x and -6x to get -7x. -7x - 9 = 5Divide to find x: Add 9 to both sides. -7x = 14Divide both sides by -7. x = -2

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Solve the system of equations by substitution. $\newline$ $-2x - 2y + z = 19$ $\newline$ $y = -8$ $\newline$ $-x + 3y - 3z = -19$

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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 - 2y + z = 19

\newline

y = -8

\newline

-x + 3y - 3z = -19

Substitute $y = -8$ : First, let's substitute $y = -8$ into the other two equations. $\newline$ $-2x - 2(-8) + z = 19$ $\newline$ $-x + 3(-8) - 3z = -19$
Simplify the equations: Now, simplify the equations. $\newline$ $-2x + 16 + z = 19$ $\newline$ $-x - 24 - 3z = -19$
Subtract and add constants: Subtract $16$ from both sides in the first equation. $\newline$ $-2x + z = 3$
Solve for $z$ : Add $24$ to both sides in the second equation. $-x - 3z = 5$
Substitute $z$ into equation: Now, let's solve for $z$ from the first equation. $z = 3 + 2x$
Distribute and combine terms: Substitute $z = 3 + 2x$ into the second equation. $\newline$ $-x - 3(3 + 2x) = 5$
Combine $x$ terms: Distribute and combine like terms. $-x - 9 - 6x = 5$
Add to isolate x: Combine $-x$ and $-6x$ to get $-7x$ . $\newline$ $-7x - 9 = 5$
Divide to find $x$ : Add $9$ to both sides. $\newline$ $-7x = 14$
Divide to find $x$ : Add $9$ to both sides. $\newline$ $-7x = 14$ Divide both sides by $-7$ . $\newline$ $x = -2$