Solve the system of equations by substitution. y = 8 2x - 2y + z = -13 -2x + y - 3z = -1 ____

Substitute y = 8: First, let's substitute y = 8 into the second and third equations. 2x - 2(8) + z = -13 -2x + 8 - 3z = -1Simplify the equations: Now, simplify the equations. 2x - 16 + z = -13 -2x + 8 - 3z = -1Add constants: Add 16 to both sides of the first simplified equation. 2x + z = 3Eliminate x: Add -8 to both sides of the second simplified equation. -2x - 3z = -9Combine equations: Now we have a system of two equations with two variables: 2x + z = 3 -2x - 3z = -9 Let's add these two equations together to eliminate x.Solve for z: Adding the equations gives us: (2x - 2x) + (z - 3z) = 3 - 9 0x - 2z = -6Substitute z = 3: Divide both sides by -2 to solve for z. z = 3Solve for x: Now we'll substitute z = 3 back into one of the two-variable equations to solve for x. 2x + 3 = 3Find y: Subtract 3 from both sides to solve for x. 2x = 0Final solution: Divide both sides by 2 to find the value of x. x = 0We have found the values for x and z. Now we substitute these values into the original equation to find y. y = 8 (given)We have the solution to the system of equations: x = 0, y = 8, z = 3

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Solve the system of equations by substitution. $\newline$ $y = 8$ $\newline$ $2x - 2y + z = -13$ $\newline$ $-2x + y - 3z = -1$

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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

y = 8

\newline

2x - 2y + z = -13

\newline

-2x + y - 3z = -1

Substitute $y = 8$ : First, let's substitute $y = 8$ into the second and third equations. $2x - 2(8) + z = -13$ $-2x + 8 - 3z = -1$
Simplify the equations: Now, simplify the equations. $2x - 16 + z = -13$ $-2x + 8 - 3z = -1$
Add constants: Add $16$ to both sides of the first simplified equation. $\newline$ $2x + z = 3$
Eliminate $x$ : Add $-8$ to both sides of the second simplified equation. $\newline$ $-2x - 3z = -9$
Combine equations: Now we have a system of two equations with two variables: $\newline$ $2x + z = 3$ $\newline$ $-2x - 3z = -9$ $\newline$ Let's add these two equations together to eliminate $x$ .
Solve for z: Adding the equations gives us: $\newline$ $(2x - 2x) + (z - 3z) = 3 - 9$ $\newline$ $0x - 2z = -6$
Substitute $z = 3$ : Divide both sides by $-2$ to solve for $z$ . $z = 3$
Solve for x: Now we'll substitute $z = 3$ back into one of the two-variable equations to solve for $x$ . $2x + 3 = 3$
Find $y$ : Subtract $3$ from both sides to solve for $x$ . $2x = 0$
Final solution: Divide both sides by $2$ to find the value of $x$ . $x = 0$
Final solution: Divide both sides by $2$ to find the value of $x$ . $x = 0$ We have found the values for $x$ and $z$ . Now we substitute these values into the original equation to find $y$ . $y = 8$ (given)
Final solution: Divide both sides by $2$ to find the value of $x$ . $\newline$ $x = 0$ We have found the values for $x$ and $z$ . Now we substitute these values into the original equation to find $y$ . $\newline$ $y = 8$ (given) We have the solution to the system of equations: $\newline$ $x = 0$ , $y = 8$ , $z = 3$