# How do you solve the following system of equations?: 4x – 5y = 14 , 2x + 15y = -4?

Jun 20, 2018

$x = 4 \left(\frac{127}{140}\right) , y = \frac{22}{35}$

#### Explanation:

$4 x - 5 y = 14 , \text{ Eqn (1)}$

$2 x + 15 y = - 4 , \text{ Eqn (2)}$

$4 x - 4 x - 5 y - 30 y = 14 + 8$, color(red)("Eqn (1) - 2 * Eqn (2)"

$- 35 y = 22 \text{ or } y = - \left(\frac{22}{35}\right)$

Substituting value of y in Eqn (1),

$4 x - 5 \cdot \left(\frac{22}{35}\right) = 14$

$4 x = 14 + 5 \left(\frac{22}{35}\right) = \frac{490 + 197}{35}$

$x = \left(\frac{687}{140}\right)$