use the elimination method to solve the following system of equations for x, y, and z. what is the value of z?
$2x + y - z = 0$
$4x - 2y + z = 4$
$-x + y = 1$
(1 point)
$z = \square$

Question

Accepted Answer

# Explanation:
## Step1: Eliminate z from first two equations
Add the first equation $2x + y - z = 0$ and the second equation $4x - 2y + z = 4$.
$$
\begin{align*}
(2x + y - z)+(4x - 2y + z)&=0 + 4\
2x+4x+y - 2y - z+z&=4\
6x - y&=4
\end{align*}
$$
## Step2: Solve for x and y
We have the equation $-x + y = 1$ (let's call it equation 3) and $6x - y = 4$ (let's call it equation 4). Add equation 3 and equation 4:
$$
\begin{align*}
(-x + y)+(6x - y)&=1 + 4\
-x+6x+y - y&=5\
5x&=5\
x&=1
\end{align*}
$$
Substitute $x = 1$ into equation 3: $-1 + y = 1$, so $y=1 + 1=2$.
## Step3: Solve for z
Substitute $x = 1$ and $y = 2$ into the first equation $2x + y - z = 0$:
$$
\begin{align*}
2(1)+2 - z&=0\
2 + 2 - z&=0\
4 - z&=0\
z&=4
\end{align*}
$$
# Answer:
$4$

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QUESTION IMAGE

Question

Explanation:

Step1: Eliminate z from first two equations

Step2: Solve for x and y

Step3: Solve for z

Answer: