# How do solve the following linear system?:  6 x+3y=11 , x+y=6 ?

Feb 10, 2016

$x = - \frac{7}{3}$, $y = \frac{25}{3}$

#### Explanation:

Please refer to some of my earlier replies. To solve a system of two linear equations in two variables you have to first eliminate one of variables.

The equations are $6 x + 3 y = 11$ and $x + y = 6$.

Multiplying latter by 3 gives us $3 x + 3 y = 18$.

Now subtracting first equation $6 x + 3 y = 11$ from $3 x + 3 y = 18$
gives us $3 x = - 7$ or $x = - \frac{7}{3}$

Putting $x = - \frac{7}{3}$ in $x + y = 6$ gives us

$y = 6 - x$ or $y = 6 - \left(- \frac{7}{3}\right)$, which gives us

$y = \frac{25}{3}$