# How do you solve the following system?: 2x +3y =5 , 8x +5y = -4

Apr 21, 2018

$X = \frac{33}{16} \mathmr{and} Y = \frac{48}{14}$

#### Explanation:

Given:
$2 x + 3 y = 5 \mathmr{and} 8 x + 5 y = - 4$
We need to make either one of the terms given, have similar coefficients to cancel out.

$\left(2 x + 3 y = 5\right)$ x $8$
$\textcolor{red}{16 x + 24 y = 40}$

$\left(8 x + 5 y = - 4\right)$ x $2$
$\textcolor{red}{16 x + 10 y = - 8}$

Subtracting one from the other, we get:
$16 x + 24 y = 40$
$- \left(16 x + 10 y = - 8\right)$

We get 14y = 48; y =48/14

Substituting y = $\frac{48}{14}$ in any one of the equations.
$2 x + \cancel{3} \left(\frac{14}{\cancel{48}}\right) = 5$
$2 x + \frac{7}{8} = 5$
$2 x = 5 - \frac{7}{8}$
$2 x = \frac{40 - 7}{8}$
$\therefore x = \frac{33}{16}$