#### Answer

See below.

#### Work Step by Step

The equations according to the text: $x+y+z=16,2x+3y+4z=46, 5x-y=31$.
$y=5x-31$, thus: $x+(5x-31)+z=16\\6x-31+z=16\\6x+z=47\\z=47-6x$
Thus: $2x+3(5x-31)+4(47-6x)=46\\2x+15x-93+188-24x=46\\-7x+95=46\\-7x=-49\\x=7$
Thus $y=5(7)-31=35-31=4$, $z=47-6(7)=47-42=5$