Answer
$x=2-2t$
$y=t$
$z=1$
Work Step by Step
Step 1.
$2x+4y-z=3$ Multiply by $1/2$
$x+2y+4z=6$
$x+2y-2z=0$ Equation 3 $+$ $(-1)$ Equation 2
Step 2.
$x+2y-\frac{1}{2}z=\frac{3}{2}$
$x+2y+4z=6$
$-6z=-6$ Multiply by $-1/6$
Step 3.
$x+2y-\frac{1}{2}z=\frac{3}{2}$
$x+2y+4z=6$
$z=1$
Step 4. Substitute $z=1$ into Equation 1 and 2
$x+2y-\frac{1}{2}=\frac{3}{2}\to x+2y=2$
$x+2y+4=6\to x+2y=2$
Step 5. Let $y=t$
$x=2-2y=2-2t$
Step 6. Conclude the solution
The solution is $x=2-2t$, $y=t$, $z=1$.
