# How do solve the following linear system?:  -6x+5y=1 , 5x-5y=10 ?

May 14, 2018

$\left(- 11 , - 13\right)$

#### Explanation:

Since you have $+ 5 y$ in one equation and $- 5 y$ in the other equation, you can add both equations to cancel out the y terms and solve for x.

$- 6 x + 5 x = - x$
$5 y - 5 y = 0$
$1 + 10 = 11$
therefore
$- x = 11$
multiplying both sides by -1:
$x = - 11$

plugging this back into the first equation:

$- 6 \left(- 11\right) + 5 y = 1$
$66 + 5 y = 1$
subtracting 66 from both sides:
$5 y = - 65$
divide both sides by 5:
$y = - 13$

putting the x-values and y-values into one point gives:
$\left(- 11 , - 13\right)$
as the solution