#### Answer

$y=5$
$x=6$

#### Work Step by Step

$y=\frac{2}{3}x+1$
$2x+3y=27$
$-\frac{2}{3}x+y=1$ (1)
$2x+3y=27$ (2)
Divide both sides of equation (2) by $3$ to obtain:
$-\frac{2}{3}x+y=1$
$\frac{2}{3}x+y=9$
___________________
$2y=10$
$y=5$
$x=6$