Solve the system of equations by substitution. 3x + 3y + 2z = -2 -x + 2y - z = 11 y = 4 ____

Solve for y: First, let's solve for y in the third equation, which is already given as y = 4.Substitute y into equations: Now, substitute y = 4 into the first and second equations. For the first equation: 3x + 3(4) + 2z = -2, which simplifies to 3x + 12 + 2z = -2. For the second equation: -x + 2(4) - z = 11, which simplifies to -x + 8 - z = 11.Solve for x or z in first equation: Next, let's solve the simplified first equation for x or z. Let's solve for x: 3x + 2z = -2 - 12, which simplifies to 3x + 2z = -14.Solve for x or z in second equation: Now, let's solve the simplified second equation for x or z. Let's solve for x: -x - z = 11 - 8, which simplifies to -x - z = 3.Express x in terms of z: We can now express x in terms of z from the second equation: -x = 3 + z, or x = -3 - z.Substitute x into first equation: Substitute x = -3 - z into the first equation: 3(-3 - z) + 2z = -14. This simplifies to -9 - 3z + 2z = -14.Combine like terms: Combine like terms: -9 - z = -14.Solve for z: Now, solve for z: -z = -14 + 9, which simplifies to -z = -5.Find x: Divide by -1 to get z: z = 5.Substitute z = 5 into x = -3 - z to find x: x = -3 - 5, which simplifies to x = -8.

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Solve the system of equations by substitution. $\newline$ $3x + 3y + 2z = -2$ $\newline$ $-x + 2y - z = 11$ $\newline$ $y = 4$

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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

3x + 3y + 2z = -2

\newline

-x + 2y - z = 11

\newline

y = 4

Solve for $y$ : First, let's solve for $y$ in the third equation, which is already given as $y = 4$ .
Substitute y into equations: Now, substitute $y = 4$ into the first and second equations. $\newline$ For the first equation: $3x + 3(4) + 2z = -2$ , which simplifies to $3x + 12 + 2z = -2$ . $\newline$ For the second equation: $-x + 2(4) - z = 11$ , which simplifies to $-x + 8 - z = 11$ .
Solve for x or z in first equation: Next, let's solve the simplified first equation for $x$ or $z$ . Let's solve for $x$ : $3x + 2z = -2 - 12$ , which simplifies to $3x + 2z = -14$ .
Solve for x or z in second equation: Now, let's solve the simplified second equation for $x$ or $z$ . Let's solve for $x$ : $-x - z = 11 - 8$ , which simplifies to $-x - z = 3$ .
Express $x$ in terms of $z$ : We can now express $x$ in terms of $z$ from the second equation: $-x = 3 + z$ , or $x = -3 - z$ .
Substitute $x$ into first equation: Substitute $x = -3 - z$ into the first equation: $3(-3 - z) + 2z = -14$ . This simplifies to $-9 - 3z + 2z = -14$ .
Combine like terms: Combine like terms: $-9 - z = -14$ .
Solve for z: Now, solve for z: $-z = -14 + 9$ , which simplifies to $-z = -5$ .
Find $x$ : Divide by $-1$ to get $z$ : $z = 5$ .
Find $x$ : Divide by $-1$ to get $z$ : $z = 5$ .Substitute $z = 5$ into $x = -3 - z$ to find $x$ : $x = -3 - 5$ , which simplifies to $x = -8$ .