# How do you solve the system using elimination 2x-y=9  and x-2y=11?

Jun 10, 2015

The solution for the system of equations is
color(blue)( x =7/3 and y =-13/3

#### Explanation:

$2 x - y = 9$ , multiplying this equation by $2$
$4 x \textcolor{b l u e}{- 2 y} = 18$.......equation $\left(1\right)$
$x \textcolor{b l u e}{- 2 y} = 11$ ........equation $\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$ to eliminate color(blue)(2y

$x \textcolor{b l u e}{\cancel{- 2 y}} = 11$
$- 4 x \textcolor{b l u e}{\cancel{+ 2 y}} = - 18$

$- 3 x = - 7$
 color(blue)(x = 7/3

Substituting $x$ in the first equation to find $y$

$y = 2 x - 9$

$y = 2. \left(\frac{7}{3}\right) - 9$

$y = \frac{14}{3} - 9$
color(blue)( y = -13/3