#### Answer

$(\displaystyle \frac{49}{11},-\frac{12}{11})$

#### Work Step by Step

If we multiply the first equation with 2,
the terms containining $y$ will be opposite in the additive sense.
$\begin{aligned}10x+6y&=38\\
x-6y&=11\end{aligned}$
Add the equations,
$ 11x=49\qquad$ ... and solve for $x$
$x=\displaystyle \frac{49}{11}$
Substitute into one of the initial equations:
$5x+3y=19$
$5(\displaystyle \frac{49}{11})+3y=19$
$3y=19-\displaystyle \frac{245}{11}$
$3y=\displaystyle \frac{209-245}{11}$
$3y=\displaystyle \frac{-36}{11}$
$y=-\displaystyle \frac{12}{11}$
Form an ordered pair $(x,y)$ as the solution to the system
$(\displaystyle \frac{49}{11},-\frac{12}{11})$