# How do solve the following linear system?:  -9x + 6y = -2 , x-3y=-2 ?

Jan 31, 2016

$\left(x , y\right) = \left(\frac{6}{7} , \frac{20}{21}\right)$

#### Explanation:

Solve by elimination:

$- 9 x + 6 y = - 2$

$x - 3 y = - 2$

We can eliminate $- 9 x$ in the first equation by $x$ in the second equation if we multiply it with $9$ to get $9 x$:

$\rightarrow 9 \left(x - 3 y = - 2\right)$

$\rightarrow 9 x - 27 y = - 18$

Now add both of the equations:

$\rightarrow \left(- 9 x + 6 y = - 2\right) + \left(9 x - 27 y = - 18\right)$

$\rightarrow - 21 y = - 20$

$\rightarrow y = \frac{- 20}{-} 21 = \frac{20}{21}$

(Because,$\frac{- n}{- p}$$= \frac{+ n}{+ p}$)

Substitute the value to the second equation:

$\rightarrow x - 3 \left(\frac{20}{21}\right) = - 2$

$\rightarrow x - \frac{60}{21} = - 2$

$\rightarrow x - \frac{20}{7} = - 2$

$\rightarrow x = - 2 + \frac{20}{7}$

$\rightarrow x = - \frac{14}{7} + \frac{20}{7}$

$\rightarrow x = \frac{6}{7}$