Answer
$(3, 2, 2)$
Work Step by Step
$2x-3y+z=2$ Equation $(1)$
$x-5y+5z=3$ Equation $(2)$
$3x+y-3z=5$ Equation $(3)$
$2\times$Equation $(2)$ $-$ Equation $(1)$
$(2x-10y+10z)-(2x-3y+z)=(6-2)$
$-7y+9z=4$ Equation $(4)$
$3\times$Equation $(2)$ $-$ Equation $(3)$
$(3x-15y+15z)-(3x+y-3z)=(9-5)$
$-16y+18z=4$ Equation $(5)$
$2\times$Equation $(4)$ $-$ Equation $(5)$
$(-14y+18z)-(-16y+18z)=(8-4)$
$2y=4$
$y=2$
Substitute $y=2$ into Equation $(4)$ to get $z$
$-7(2)+9z=4$
$-14+9z=4$
$9z=18$
$z=2$
Substitute known values for $y$ and $z$ into Equation $(1)$ to get $x$
$2x-3(2)+2=2$
$2x-4=2$
$2x=6$
$x=3$
$(3, 2, 2)$ satisfies the given equations.
Solution is $(3, 2, 2)$
