# How do solve the following linear system?:  x+y=6 , 6x=29-8y ?

From the ${1}^{s t}$ eqn., we have, $x = 6 - y \ldots \ldots . . \left(1\right)$
Sub.ing this in the ${2}^{n d}$ eqn., we get, $6 \left(6 - y\right) = 29 - 8 y ,$ i.e., $36 - 6 y = 29 - 8 y ,$ or, $36 - 29 = 6 y - 8 y .$
$\therefore 7 = - 2 y ,$ giving, $y = - \frac{7}{2.}$
Now from $\left(1\right)$, we get, $x = 6 + \frac{7}{2} = \frac{19}{2.}$
Hence, the soln. is $x = \frac{19}{2} , y = - \frac{7}{2.}$