# How do solve the following linear system?:  x+2y=1 , 6x=29-8y ?

Feb 3, 2016

$x = \frac{25}{2}$ $y = - \frac{23}{4}$

#### Explanation:

suppose,
$x + 2 y = 1. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left(i\right)$
$6 x = 29 - 8 y \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left(i i\right)$

from $\left(i i\right)$ we can find,

$6 x + 8 y = 29. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left(i i i\right)$

now,
$6 \times \left(i\right) - \left(i i i\right) \implies$
$\cancel{6 x} + 12 y = 6$
$\cancel{6 x} + 8 y = 29$
...............................
$\implies 4 y = - 23$
$\implies y = - \frac{23}{4}$

now, putting $y = - \frac{23}{4}$ in $\left(i i i\right)$ we get,

$6 x - 46 = 29$

$\implies 6 x = 75$

$\implies x = \frac{25}{2}$