# How do you solve the following system: 4x+y=-7, 10y=42+2x ?

May 23, 2017

Follow explanation. $x = - \frac{8}{3}$ and $y = \frac{11}{3}$

#### Explanation:

From the second equation you can get
$y = 4.2 + \left(\frac{x}{5}\right)$ when you divide the equation by 10.

Now put this value on the first equation:

$4 x + 4.2 + \frac{x}{5} = - 7$

You have one unknown (x) and one equation.

$21 \frac{x}{5} = - 7 - 4.2$

$21 x = 5 \cdot \left(- 11.2\right)$
$21 x = - 56$
$x = - \frac{56}{21}$
$x = - \frac{8}{3}$

Now you can put this value on the second equation:

$10 y = 42 + 2 \cdot \left(- \frac{8}{3}\right)$
$10 y = 42 - \frac{16}{3}$
$10 y = \frac{110}{3}$
$y = \frac{110}{30}$
or
$y = \frac{11}{3}$