Answer
$x = \frac 5 3$ and $y = \frac 1 3$
Work Step by Step
1. Notice that, if we add the two equations, neither $x$ or $y$ will be eliminated. But, if we multiply the first equation by 2, the $y$ unknown will be eliminated:
$2(0.2x - 0.1y) = 2(0.3)$
$0.2x + 0.2y = 0.4$
$0.4x - 0.2y = 0.6$
$0.2x + 0.2y = 0.4$
Adding the equations:
$0.4x + 0.2x - 0.2y + 0.2y = 0.6 + 0.4$
$0.6x = 1$
$\frac{0.6x}{0.6} = \frac{1}{0.6}$
$x = \frac{1}{0.6} = \frac{10}{6} = \frac 5 3$
2. Calculate the $y$ value by substituting the value for $x$ on the first equation:
$0.2 (\frac{5}{3}) - 0.1y = 0.3$
$\frac{1}{3} - 0.1y = 0.3$
$\frac{1}{3} - 0.3 = 0.1y$
$\frac 1 3 - \frac {0.9} {3} = 0.1y$
$\frac {0.1} 3 = 0.1y$
$\frac 1 3 = y$
