#### Answer

$( 10.5,6.5)$

#### Work Step by Step

To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 5:$
$\left\{\begin{array}{llll}
-0.3x & +0.5y & =0.1 & /\times 10\\
0.1x & -0.1y & =0.4 & /\times 50
\end{array}\right.$
$\left\{\begin{array}{llll}
-3x & +5y & =1 & \\
5x & -5y & =20 &
\end{array}\right.$
... add and solve ...
$ 2x=21\qquad/\div 2$
$x=\displaystyle \frac{21}{2}$
Back substitute into one of the above equations:
$5x-5y=20$
$5\displaystyle \cdot\frac{21}{2}-5y=20\qquad /\times 2$
$105-10y=40\qquad /-105 $
$-10y=-65\qquad/\div(-10)$
$y=6.5$
Solutions are ordered pairs (x,y):
$( 10.5,6.5)$
Check graphically by graphing both lines in the same window and determining the intersection (see image).