# How do you solve the following system?: 7x +2y =-2 , -4x +5y = 4

Mar 29, 2018

$x = - \frac{18}{43}$ and $y = \frac{20}{43}$

#### Explanation:

$4 \cdot \left(7 x + 2 y\right) + 7 \cdot \left(- 4 x + 5 y\right) = 4 \cdot \left(- 2\right) + 7 \cdot 4$

$28 x + 8 y - 28 x + 35 y = - 8 + 28$

$43 y = 20$ , so $y = \frac{20}{43}$

Hence,

$- 4 x + 5 \cdot \frac{20}{43} = 4$

$- 4 x = \frac{172 - 100}{43}$

$- 4 x = \frac{72}{43}$, so $x = - \frac{18}{43}$