# How do you solve the following system: 7y - 2x = 10, -5x − y = 14 ?

Jan 28, 2016

$y = \frac{22}{37}$ and $x =$-108/37#

#### Explanation:

Let's solve the second equation for y, which should be simply since it doesn't have a coefficient. It starts off as:

$- 5 x - y = 14$

Add y to both sides and subtract 14 from both sides:

$- 5 x - 14 = y$, or in reverse: $y = - 5 x - 14$.

Now we can plug that into the second equation:

$7 \left(- 5 x - 14\right) - 2 x = 10$

Multiply through: (tip: $7 \cdot 14$ is $98$)
$- 35 x - 98 - 2 x = 10$

Consolidate $x$'s:
$- 37 x - 98 = 10$

Add $98$ to both sides:
$- 37 x = 108$

Divide by $- 37$:
$x = \frac{108}{-} 37$

Now plug that back into the initial equation:
$- 5 \cdot \frac{108}{-} 37 - y = 14$
$\frac{540}{37} - y = 14$

Add $y$ and subtract $14$:
$\frac{540}{37} - 14 = y$

Get a common denominator for $14$:
$\frac{540}{37} - \frac{518}{37} = y$

Subtract:
$\frac{22}{37} = y$