# How do solve the following linear system?:  3x-8y=6, 2x - 5y=3 ?

Jun 23, 2017

By some arrangement, $x = - 6$ and $y = - 3$

#### Explanation:

Expand the first original equation with $2$ and the second original equation with $- 3$ to get only equation having one unknown:

$6 x - 16 y = 12$
#-6x + 15 y = -9

Add the terms (of the above equations, yielding
$- 16 y + 15 y = 12 - 9$

$- y = 3$

or $y = - 3$

Now put this value in any equation (for example the first equation):

$3 x - \left(8 \times - 3\right) = 6$

$3 x + 24 = 6$

$3 x = 6 - 24$

$3 x = - 18$

$x = - 6$

This is your answer: $x = - 6$ and $y = - 3$