Answer
$(2-2t, t, 1)$
Work Step by Step
The question asks to find the solution to the system of equations.
Given:
1. $2x + 4y - z = 3$
2. $x + 2y + 4z = 6$
3. $x + 2y - 2z = 0$
Subtract equation 3 from 2
$x + 2y + 4z = 6$
- ($x + 2y - 2z = 0$)
$6z = 6$
$z = 1$
Now the issue is that there are infinite solutions for x and y to suffice these equations (since each equation has a multiple of respective x's and y's). Thus set $y= t$.
Thus $x + 2t - 2 = 0$ (from equation 3)
$x = 2 - 2t$
Solution: $(2-2t, t, 1)$
