# How do you solve the system 3x-2y=2 and 5x-5y=10?

Jun 10, 2015

The solution for the system of equation is
 color(red)(x = -2 , y=-4

#### Explanation:

$3 x - 2 y = 2$ ,multiplying the equation by $5$
$15 x - \textcolor{red}{10 y} = 10$...........equation $1$

$5 x - 5 y = 10$ , multiplying the equation by $2$
$10 x - \textcolor{red}{10 y} = 20$.......equation $2$

Subtracting equation $1$ from $2$ to eliminate color(red)(10y
$10 x - \cancel{\textcolor{red}{10 y}} = 20$
$- 15 x + \cancel{\textcolor{red}{10 y}} = - 10$

$- 5 x = 10$
color(red)( x = -2

Substituting $x$ in equation $1$ to find $y$
$3 x - 2 = 2 y$
$\frac{3 x - 2}{2} = y$

$y = \frac{3. \left(- 2\right) - 2}{2}$
$y = - \frac{8}{2} = - 4$
 color(red)(y=-4