# How do solve the following linear system?:  5x+2y=1 , 2/3x + 4y = -1 ?

Jan 27, 2016

$x = \frac{9}{28}$

$y = \frac{17}{45}$

#### Explanation:

Rearrange one of the equations to get a variable on its own on the left hand side, then substitute it into the other equation and solve.

$5 x + 2 y = 1$
$\frac{2}{3} x + 4 y = - 1$
$2 y = 1 - 5 x$
$y = \frac{1}{2} - \frac{5}{2} x$

Substituting into he second equation
$\frac{2}{3} x + 4 \left(\frac{1}{2} - \frac{5}{2} x\right) = - 1$
$\frac{2}{3} x + 2 - 10 x = - 1$
$2 x - 30 x = - 9$
$x = \frac{- 9}{- 28} = \frac{9}{28}$

Then $y = \frac{1}{2} - \frac{5}{2} \cdot \left(\frac{9}{28}\right)$
$y = \frac{28 - 45}{56} = \frac{17}{45}$