# How do you solve the following system: 5x - 7y = 12 , x + 8y = 15 ?

May 21, 2016

The solution for the system of equations is:
color(green)(x=201/47 , y = 63/47

#### Explanation:

$\textcolor{b l u e}{5 x} - 7 y = 12$.............equation $\left(1\right)$

$x + 8 y = 15$, multiplying by $5$
$\textcolor{b l u e}{5 x} + 40 y = 75$ ..........equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from equation $1 :$

$\cancel{\textcolor{b l u e}{5 x}} - 7 y = 12$
$- \cancel{\textcolor{b l u e}{5 x}} - 40 y = - 75$

$- 47 y = - 63$

$y = - \frac{63}{47}$

color(green)(y = 63/47

Finding $x$ from equation $2$
$x + 8 y = 15$

$x = 15 - 8 y$

$x = 15 - 8 \cdot \left(\frac{63}{47}\right)$

$x = 15 - \frac{504}{47}$

$x = \frac{705}{47} - \frac{504}{47}$

color(green)(x = 201/47