Answer
Solution:$(5,1,-2,1)$
Work Step by Step
$5x+4y=29$ Equation $(1)$
$y+z-w = -2$ Equation $(2)$
$5x+z = 23$ Equation $(3)$
$y-z+w = 4$ Equation $(4)$
Adding Equation $(2)$ and Equation $(4)$
$y+y+z-z-w+w = -2+4$
$2y = 2$
$y = 1$
Substituting $y$ value in Equation $(1)$
$5x+4y=29$
$5x+4(1)=29$
$5x+4 = 29$
$5x= 29-4$
$5x= 25$
$x=5$
Substituting $x$ value in Equation $(3)$
$5x+z = 23$
$5(5)+z = 23$
$25+z = 23$
$z=23-25$
$z= -2$
Substituting $z$ and $y$ values in Equation $(4)$
$y-z+w = 4$
$1-(-2)+w = 4$
$1+2+w = 4$
$3+w = 4$
$w = 1$
Solution:$(x,y,z,w) = (5,1,-2,1)$