#### Answer

$x=7$
$y=1$
(7, 1)

#### Work Step by Step

$\frac{x-1}{2}+\frac{y+2}{3}=4$
$x-2y=5$
Multiply both sides of the first equation by 6 to get rid of the fractions.
$\frac{x-1}{2}*6+\frac{y+2}{3}*6=4*6$
$3x-3+2y+4=24$
$3x + 2y = 23$
Add the second equation to the multiplied first equation.
$3x + 2y +(x-2y)=23+5$
$3x+x+2y-2y=28$
$4x=28$
$x=7$
Substitute x in the second equation to get y.
$7-2y=5$
$-2y=-2$
$y=1$