Answer
$(1,2,-2)$
Work Step by Step
$5x+y+3z=1$ Equation $(1)$
$x-y+3z=-7$ Equation $(2)$
$-x+y=1$ Equation $(3)$
Add Equation $(2)$ and Equation $(3)$
$x-y+3z-x+y=-7+1$
$3z = -6$
$z=-2$
Add Equation $(1)$ and Equation $(2)$
$5x+y+3z+x-y+3z=1-7$
$6x+6z=-6$
$x+z=-1$ Equation $(4)$
Substitute $z$ value in Equation $(4)$ to get $x$
$x+z=-1$
$x-2=-1$
$x=-1+2$
$x=1$
Substitute $x$ value in Equation $(3)$ to get $y$
$-x+y=1$
$-1+y=1$
$y=1+1$
$y=2$
$(1,2,-2)$ satisfies the given equations.
Solution is $(1,2,-2)$
