Answer
$(-3,-35,-7)$
Work Step by Step
$6x-5z=17$ Equation $(1)$
$5x-y+3z=-1$ Equation $(2)$
$2x+y=-41$ Equation $(3)$
Add Equation $(2)$ and Equation $(3)$
$5x-y+3z+2x+y=-1-41$
$7x+3z = -42$ Equation $(4)$
Multiply Equation $(1)$ by $3$
$3(6x-5z)=3(17)$
$18x-15z=51$ Equation $(5)$
Multiply Equation $(4)$ by $5$
$5(7x+3z) =5( -42)$
$35x+15z = -210$ Equation $(6)$
Add Equation $(5)$ and Equation $(6)$ to find $x$
$18x-15z+35x+15z=51-210$
$53x=-159$
$x=-3$
Substitute $x$ value in Equation $(3)$ to find $y$
$2x+y=-41$
$2(-3)+y=-41$
$-6+y=-41$
$y=-41+6$
$y=-35$
Substitute $x$ value in Equation $(1)$ to find $z$
$6x-5z=17$
$6(-3)-5z=17$
$-18-5z=17$
$-5z=17+18 $
$-5z=35$
$z=-7$
Solution: $(-3,-35,-7)$
