Answer
$(6,22,-20)$
Work Step by Step
$x+y+z=8$ Equation $(1)$
$2x-y-z=10$ Equation $(2)$
$x-2y-3z=22$ Equation $(3)$
Add Equation $(1)$ and Equation $(2)$
$x+y+z+2x-y-z=8+10$
Combine like terms.
$3x=18$
$x= 6$
Multiply Equation $(1)$ by $2$ and add with Equation $(3)$
$2(x+y+z)+x-2y-3z=2(8)+22$
$2x+2y+2z+x-2y-3z=16+22$
Combine like terms.
$3x-z=38$ Equation $(4)$
Substitute $x$ value in Equation $(4)$ to get $z$ value.
$3x-z=38$
$3(6)-z=38$
$18-z=38$
$-z=38-18$
$-z=20$
$z=-20$
Substitute $x$ and $z$ values in Equation $(3)$ to get $y$ value.
$x-2y-3z=22$
$6-2y-3(-20)=22$
$6-2y+60=22$
$-2y+66=22$
$-2y=22-66$
$-2y=-44$
$y=22$
$(6,22,-20)$ satisfies the given equations.
Solution:$(6,22,-20)$
