Answer
$x_1=t$
$x_2=\frac{-3}{2}t$
$x_3=\frac{1}{2}t$
Work Step by Step
Equation 1: $x_1 - 2x_2 - 8x_3=0$
Equation 2: $3x_1+2x_2=0$
Adding the second equation to the first equation produces a new first equation
$4x_1-8x_3=0$
$3x_1+2x_2=0$
Then
$x_1=2x_3$
$x_1=\frac{-2}{3}x_2$
To represent the solutions, choose $x_1$ to be the free variable and represent it by the parameter $t$ because and you can describe the solution set as
$t=2x_3$
$t=\frac{-2}{3}x_2$
Then:
$x_1=t$
$x_2=\frac{-3}{2}t$
$x_3=\frac{1}{2}t$
