# What is the value of y in the solution to the following system of equations 5x-3y=-112, x-6y=-14?

Jan 7, 2017

$y = - \frac{52}{27}$

#### Explanation:

To solve for an unknown you need to manipulate things so that you just 1 unknown

I chose to get rid of $x$ as we need to have just the unknown of $y$

Given:

$5 x - 3 y = - 122 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left(1\right)$
$\textcolor{w h i t e}{5} x - 6 y = - 14 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(2\right)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider $E q u a t i o n \left(2\right)$

Add $6 y$to both sides giving:

$x = 6 y - 14 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(3\right)$

Using equation(3) substitute for $x$ in equation(1)

color(green)(5color(red)(x)-3y=-122" "->" "5(color(red)(6y-14))-3y=-122

$\text{ } \textcolor{g r e e n}{30 y - 70 - 3 y = - 122}$

$\text{ } \textcolor{g r e e n}{27 y - 70 = - 122}$

" "color(green)(27y=-122+70
$\text{ } \textcolor{g r e e n}{27 y = - 52}$
$\text{ } \textcolor{g r e e n}{y = - \frac{52}{27}}$