Answer
Solution set is $\{ (x,y,z) | x-y+3z =2\}$.
Work Step by Step
$x-y+3z = 2$ Equation $(1)$
$-2x+2y-6z = -4$ Equation $(2)$
$3x-3y+9z = 6$ Equation $(3)$
Multiply Equation $(1)$ by $2$
$2x-2y+6z = 4$ Equation $(4)$
Adding Equation $(2)$ and Equation $(4)$
$-2x+2x +2y-2y -6z+6z = -4+4$
$0=0$
This statement is true for all values of $x,y$ and $z$. There are infinitely many solutions.
The solution set is $\{ (x,y,z) | x-y+3z =2\}$