How do you solve the system?: 2(x-4) + y=6, 3x-2(y-3)=13

Nov 2, 2015

$x = 5 , y = 4$

Explanation:

Nov 2, 2015

First expand the system and then use simultaneous equations to get $x = 5$ and $y = 4$

Explanation:

Expanding and simplifying the system

$2 \left(x - 4\right) + y = 2 x - 8 + y = 6$

Therefore,
$2 x + y = 14$ $\left(1\right)$

$3 x - 2 \left(y - 3\right) = 3 x - 2 y + 6 = 13$

Therefore,
$3 x - 2 y = 7$ $\left(2\right)$

Simultaneous Equations

(2 $\times$ $\left(1\right)$) $+$ $\left(2\right)$

$4 x + 2 y + 28$ $\left(1\right)$
$3 x - 2 y = 7$ $\left(2\right)$

Cancel out the $y$ terms and equate:

$7 x = 35$
$x = 5$

Sub $x$ back into $\left(1\right)$:

$2 \left(5\right) + y = 14$
$y = 4$