#### Answer

$x_{1}=-\frac{1}{2}$
$x_{2}=\frac{4}{5}$
$(-\frac{1}{2},\frac{4}{5})$

#### Work Step by Step

$0.2x_{1}+0.3x_{2}=0.14$
$0.4x_{1}+0.5x_{2}=0.20$
Multiply the first equation by $-2$.
$-0.4x_{1}-0.6x_{2}=-0.28$
$0.4x_{1}+0.5x_{2}=0.2$
Eliminate the $x_{1}$-variable by addition of the two equations.
$-0.1x_{2}=-0.08$
$x_{2}=0.8=\frac{4}{5}$
Substitute for $x_{2}$ and solve for $x_{1}$.
$0.2x_{1}+0.3\times0.8=0.14$
$0.2x_{1}=-0.1$
$x_{1}=-0.5=-\frac{1}{2}$