#### Answer

$( \displaystyle \frac{5}{3},-\frac{4}{3})$

#### Work Step by Step

To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 2:$
$\left\{\begin{array}{llll}
0.5x & +0.1y & =0.7 & /\times 20\\
0.2x & -0.2y & =0.6 & /\times 10
\end{array}\right.$
$\left\{\begin{array}{llll}
10x & +2y & =14 & \\
2x & -2y & =6 &
\end{array}\right.$
... add and solve ...
$12x=20\qquad/\div 7$
$x=\displaystyle \frac{20}{12}=\frac{5}{3}$
Back substitute into one of the above equations:
$2x-2y=6$
$2\displaystyle \cdot\frac{5}{3}-2y=6\qquad /\times 3$
$10-6y=18\qquad /-10 $
$-6y=8\qquad/\div(-6)$
$y=-\displaystyle \frac{8}{6}=-\frac{4}{3}$
Solutions are ordered pairs (x,y):
$( \displaystyle \frac{5}{3},-\frac{4}{3})$
Check graphically by graphing both lines in the same window and determining the intersection (see image).