Answer
$x = 3, y = -4$
Work Step by Step
Solving for $x$ in $-2x = 6y + 18 $ gives $x = -3y - 9$
Plug this into the $x$ in $-29 = 5y - 3x$ to obtain:
$-29 = 5y - 3(-3y - 9 )
\\-29 = 5y + 9y + 27
\\-56 = 14y
\\y = -4$
Plug $-4$ to the $y$ in $x = -3y - 9$ to obtain:
$x = -3(-4) - 9
\\x=12-9
\\x= 3$