# How do you solve the following system: 10y=42+2x , 3x - 3y = 2 ?

Aug 31, 2016

$y = \frac{65}{12} \mathmr{and} x = \frac{73}{12}$

#### Explanation:

$x - y = \frac{2}{3}$

or $x = y + \frac{2}{3}$

$10 \cdot y = 42 + 2 \cdot \left(y + \left(\frac{2}{3}\right)\right)$

$10 \cdot y - 2 \cdot y = 42 + \frac{4}{3}$

$8 \cdot y = \frac{126 + 4}{3}$

$8 \cdot y = \frac{130}{3}$

$y = \frac{130}{8 \cdot 3}$

$y = \frac{65}{12}$

After this step, you can solve x:

$x = \frac{65}{12} + \frac{2}{3}$

or $x = \frac{65 + 8}{12}$

$x = \frac{73}{12}$