#### Answer

x = 14
y = -2
(14, -2)

#### Work Step by Step

$\frac{x-2}{4}+\frac{y-1}{3}=2$
$x-3y=20$
Express x in terms of y.
$x=20+3y$
Substitute for x in the first equation and solve for y.
$\frac{(20+3y)-2}{4}+\frac{y-1}{3}=2$ $\rightarrow$ Simplify.
$\frac{18+3y}{4}+\frac{y-1}{3}=2$ $\rightarrow$ Multiply both sides by 12 to remove the fractions.
$3(18+3y)+ 4(y-1)=24$ $\rightarrow$ Simplify.
$54 + 9y + 4y -4 = 24$
$13y = -26$
$y = -2$
Substitute for y and solve for x.
$x-3y = 20$
$x-3(-2)=20$
$x = 14$