Answer to Question #175575 in Linear Algebra for william

Question

solve the system of linear equations.

x-y + 2z = 5

2x - 2y + 4z = 10

3x - 3y + 6z = 15

Answer 1

$x-y+2z=5\\ 2x-2y+4z=10\\ 3x-3y+6z=15$ $\Darr$ $x-y+2z=5\\ 2x-2y+4z=10\space|\space/2\\ 3x-3y+6z=15\space|\space/3$ $\Darr$ $x-y+2z=5\\ x-y+2z=5\\ x-y+2z=5$ $\Darr$ $x-y+2z=5$

Answer: ($y-2z+5$; $y$; $z$) where $y\space\epsilon\spaceℝ$, $z\space\epsilon\spaceℝ$.