# How do solve the following linear system?:  2x+6y=5 , -x - y = 8 ?

Feb 16, 2017

$x = - \frac{53}{4}$ and $y = \frac{21}{4}$

#### Explanation:

We have two equations here

$2 x + 6 y = 5$ **......................(1) and

$- x - y = 8$ **......................(2)

Observe that we have $2 x$ in first equation and $- x$ in second equation. So if we double (2) and add to (1), $x$ will be eliminated and we get

$2 x + 6 y - 2 x - 2 y = 5 + 16$ or $4 y = 21$ i.e. $y = \frac{21}{4}$

putting this value in (2), we get

$- x - \frac{21}{4} = 8$ or $- x = 8 + \frac{21}{4} = \frac{32 + 21}{4} = \frac{53}{4}$

and $x = - \frac{53}{4}$