# How do you solve the following system?:  2x+5=-9y , 2x -5y=7

Feb 14, 2016

The solution for the system of equations is :
$x = \frac{19}{14}$

$y = - \frac{6}{7}$

#### Explanation:

$\textcolor{b l u e}{2 x} + 9 y = - 5$......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 $1$

$\cancel{\textcolor{b l u e}{2 x}} + 9 y = - 5$

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

$14 y = - 12$

$y = - \frac{12}{14}$

$y = - \frac{6}{7}$

Finding $x$ from equation $1$
$2 x + 9 y = - 5$

$2 x + 9 \times \left(- \frac{6}{7}\right) = - 5$

$2 x - \frac{54}{7} = - 5$

$2 x = - 5 + \frac{54}{7}$

$2 x = - \frac{35}{7} + \frac{54}{7}$

$2 x = \frac{19}{7}$

$x = \frac{19}{7 \times 2}$

$x = \frac{19}{14}$