Answer
We can eliminate x from equations $1$ and $2$ by multiplying equation $1$ by $-2\text{ }$ and adding the equations. We can eliminate x from equations 1 and 3 by multiplying equation $1$ by $-4$ and adding the equations.
Work Step by Step
Let us consider the equations:
$x+y-z=-1$ Equation 1
$2x-2y-5z=7$ Equation 2
$4x+y-2z=7$ Equation 3
Now, eliminate x from equations (I) and (II) by multiplying (I) by $-2$ to get;
$\begin{align}
& -2x+\left( -2 \right)y+2z=-1\left( -2 \right) \\
& -2x-2y+2z=2 \\
\end{align}$
Then, add this equation with equation (II) to get;
$\begin{align}
& -2x-2y+2z+\left( 2x-2y-5z \right)=2+7 \\
& -4y-3z=9
\end{align}$
Therefore, x is eliminated from equations (I) and (II).
Then, eliminate x from equations (I) and (III) by multiplying (I) by $-4$ to get;
$\begin{align}
& x\cdot \left( -4 \right)+y\cdot \left( -4 \right)-z\cdot \left( -4 \right)=-1\cdot \left( -4 \right) \\
& -4x-4y+4z=4
\end{align}$
Then, add this equation with (III) to get;
$\begin{align}
& -4x-4y+4z+4x+y-2z=4+7 \\
& -3y+2z=11
\end{align}$
Thus, it is clear from this equation that x is eliminated from equations (I) and (III).
