Answer
$x=2-2t$
$y=-\frac{2}{3}+\frac{4}{3}t$
$z=t$
Work Step by Step
Step 1.
$x+3y-2z=0$
$2x+4z=4$ Equation 2 $+$ $(-2)$ Equation 1
$4x+6y=4$ Equation 3 $+$ $(-4)$ Equation 1
Step 2.
$x+3y-2z=0$ Equation 1 $+$ $\frac{1}{2}$ Equation 2
$-6y+8z=4$ Multiply by $-\frac{1}{6}$
$-6y+8z=4$ Equation 3 $+$ $(-1)$ Equation 2
Step 3.
$x+2z=2$
$y-\frac{4}{3}z=-\frac{2}{3}$
Step 4. Let $z=t$
$x=2-2z=2-2t$
$y=-\frac{2}{3}+\frac{4}{3}z=-\frac{2}{3}+\frac{4}{3}t$
Step 5. Conclude the solution
The solution is $x=2-2t$, $y=-\frac{2}{3}+\frac{4}{3}t$, $z=t$.
