# How do solve the following linear system?:  2x-y=4 , 3x – 4y = 7 ?

Feb 3, 2017

$x = \frac{9}{5}$
$y = - \frac{2}{5}$

#### Explanation:

Given -

$2 x - y = 4$------------------(1)
$3 x - 4 y = 7$-----------------(2)

Solve equation (1) for $y$

$2 x - y = 4$
$- y = 4 - 2 x$
$y = - 4 + 2 x$

Substitute $y = - 4 + 2 x$ in equation (2)

$3 x - 4 y = 7$
$3 x - 4 \left(- 4 + 2 x\right) = 7$
$3 x + 16 - 8 x = 7$
$- 5 x = 7 - 16 = - 9$
$x = \frac{- 9}{- 5} = \frac{9}{5}$
$x = \frac{9}{5}$

Substitute $x = \frac{9}{5}$ in eqation (1)

$2 x - y = 4$
$2 \left(\frac{9}{5}\right) - y = 4$
$\frac{18}{5} - y = 4$
$- y = 4 - \frac{18}{5}$
$- y = \frac{20 - 18}{5} = \frac{2}{5}$
$y = - \frac{2}{5}$