Solve the system of equations by substitution. -2x - 3y + 3z = -4 y = 4 x + y - z = -1 ____

Substitute y = 4: Substitute y = 4 into -2x - 3y + 3z = -4. -2x - 3(4) + 3z = -4 -2x - 12 + 3z = -4Add 12 to isolate: Add 12 to both sides to isolate terms with variables. -2x + 3z = -4 + 12 -2x + 3z = 8Substitute y = 4: Substitute y = 4 into x + y - z = -1. x + 4 - z = -1Subtract 4 to isolate: Subtract 4 from both sides to isolate terms with variables. x - z = -1 - 4 x - z = -5Solve for x: Now we have two equations: 1) -2x + 3z = 8 2) x - z = -5 Let's solve equation 2) for x. x = z - 5Substitute x = z - 5: Substitute x = z - 5 into equation 1). -2(z - 5) + 3z = 8 -2z + 10 + 3z = 8Combine like terms: Combine like terms. z + 10 = 8Subtract 10 for z: Subtract 10 from both sides to solve for z. z = 8 - 10 z = -2Substitute z = -2: Substitute z = -2 into x = z - 5. x = -2 - 5 x = -7Find all three values: We already have y = 4 from the given equation. So, we have found all three values: x = -7, y = 4, z = -2

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Solve the system of equations by substitution. $\newline$ $-2x - 3y + 3z = -4$ $\newline$ $y = 4$ $\newline$ $x + y - z = -1$

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

-2x - 3y + 3z = -4

\newline

y = 4

\newline

x + y - z = -1

Substitute $y = 4$ : Substitute $y = 4$ into $-2x - 3y + 3z = -4$ .
$-2x - 3(4) + 3z = -4$
$-2x - 12 + 3z = -4$
Add $12$ to isolate: Add $12$ to both sides to isolate terms with variables. $\newline$ $-2x + 3z = -4 + 12$ $\newline$ $-2x + 3z = 8$
Substitute $y = 4$ : Substitute $y = 4$ into $x + y - z = -1$ . $\newline$ $x + 4 - z = -1$
Subtract $4$ to isolate: Subtract $4$ from both sides to isolate terms with variables. $\newline$ $x - z = -1 - 4$ $\newline$ $x - z = -5$
Solve for x: Now we have two equations: $\newline$ $1$ ) $-2x + 3z = 8$ $\newline$ $2$ ) $x - z = -5$ $\newline$ Let's solve equation $2$ ) for x. $\newline$ $x = z - 5$
Substitute $x = z - 5$ : Substitute $x = z - 5$ into equation $1$ ). $-2(z - 5) + 3z = 8$ $-2z + 10 + 3z = 8$
Combine like terms: Combine like terms. $z + 10 = 8$
Subtract $10$ for $z$ : Subtract $10$ from both sides to solve for $z$ . $z = 8 - 10$ $z = -2$
Substitute $z = -2$ : Substitute $z = -2$ into $x = z - 5$ . $\newline$ $x = -2 - 5$ $\newline$ $x = -7$
Find all three values: We already have $y = 4$ from the given equation. $\newline$ So, we have found all three values: $\newline$ $x = -7$ , $y = 4$ , $z = -2$