# How do solve the following linear system?:  3x-2y=2 , -6x+5y=1 ?

Feb 1, 2016

Solve by substitution and elimination:

$3 x - 2 y = 2$

$- 6 x + 5 y = 1$

We can eliminate $- 6 x$ from the second equation by $3 x$ in the first equation if we multiply it with $2$ to get $6 x$.

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

$\rightarrow = 6 x - 4 y = 4$

$\rightarrow \left(- 6 x + 5 y = 1\right) + \left(6 x - 4 y = 4\right)$

$\rightarrow \left(5 y = 1\right) + \left(- 4 y = 4\right)$

$\rightarrow y = 5$

Substitute the value of $y$ to the second equation:

$\rightarrow - 6 x + 5 \left(5\right) = 1$

$\rightarrow - 6 x + 25 = 1$

$\rightarrow - 6 x = 1 - 25$

$\rightarrow - 6 x = - 24$

$\rightarrow x = \frac{- 24}{-} 6 = \frac{24}{6} = 4$

Because,$\frac{- n}{-} m = \frac{n}{m}$

So,$\left(x , y\right) = \left(4 , 5\right)$