# How do you solve the following system?:  x - y = -6, 2x -5y=7

Mar 13, 2016

The solution for the system of equations is:
color(green)(x=-37/3

color(green)(y= (-19)/3

#### Explanation:

$x - y = - 6$, multiplying this equation by $2$
$\textcolor{b l u e}{2 x} - 2 y = - 12$...............equation $\left(1\right)$

$\textcolor{b l u e}{2 x} - 5 y = 7$........................equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from $1$ results in elimination of $\textcolor{b l u e}{2 x}$ from the equations.

$\cancel{\textcolor{b l u e}{2 x}} - 2 y = - 12$
$- \cancel{\textcolor{b l u e}{2 x}} + 5 y = - 7$

$3 y = - 19$

color(green)(y= (-19)/3

Finding the value of $x$ from equation $1$:

$x - y = - 6$

$x = - 6 + y$

$x = - 6 + \textcolor{g r e e n}{\left(\frac{- 19}{3}\right)}$

$x = - \frac{18}{3} + \left(\frac{- 19}{3}\right)$

color(green)(x=-37/3