Answer
$(1,1,0,2)$
Work Step by Step
$x+y-w=0$ Equation $(1)$
$y+2z+w=3$ Equation $(2)$
$x-z=1$ Equation $(3)$
$2x-y-w=-1$ Equation $(4)$
Adding Equation $(2)$ and Equation $(4)$ we get,
$y+2z+w+2x-y-w=3-1$
$2x+2z = 2$
$x+z = 1$ Equation $(5)$
Adding Equation $(3)$ and Equation $(5)$ we get,
$x-z+x+z=1+1$
$2x=2$
$x=1$
Substituting $x$ value in Equation $(3)$
$x-z=1$
$1-z=1$
$-z=1-1$
$-z=0$
$z=0$
Adding Equation $(1)$ and Equation $(2)$ we get,
$x+y-w+y+2z+w=0+3$
$x+2y+2z=3$ Equation $(6)$
Substituting $x$ and $z $ values in Equation $(6)$
$x+2y+2z=3$
$1+2y+2(0)=3$
$1+2y+0=3$
$2y=2$
$y=1$
Substituting $x$ and $y$ values in Equation $(1)$
$x+y-w=0$
$1+1-w=0$
$2-w=0$
$-w=-2$
$w=2$
$(1,1,0,2)$ satisfies the given equations.
Solution: $(1,1,0,2)$