How do you solve the following system: x-2y=3, -6x + y = -8 ?

Feb 13, 2016

The solution for the system of equations is:

$x = \frac{13}{11}$
$y = - \frac{10}{11}$

Explanation:

$x - \textcolor{b l u e}{2 y} = 3$....................equation $\left(1\right)$

$- 6 x + y = - 8$, multiplying by $2$
$- 12 x + \textcolor{b l u e}{2 y} = - 16$.......equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$

$x - \cancel{\textcolor{b l u e}{2 y}} = 3$

$- 12 x + \cancel{\textcolor{b l u e}{2 y}} = - 16$

$- 11 x = - 13$

$x = \frac{- 13}{- 11}$

$x = \frac{13}{11}$

Finding $y$ from equation $1$
$x - 2 y = 3$

$2 y = x - 3$

$2 y = \frac{13}{11} - 3$

$2 y = \frac{13}{11} - \frac{33}{11}$

$2 y = - \frac{20}{11}$

$y = - \frac{\cancel{20}}{11 \times \cancel{2}}$

$y = - \frac{10}{11}$