# How do you solve the following equations by substitution?: 5x - 2y = -5 and y - 5x = 3?

May 9, 2018

color(indigo)(x = -1/5, y = 2

#### Explanation:

5x - 2y = -5, " Eqn (1)

$5 x = 2 y - 5$

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

-5x + y = 3, " Eqn (2)

Substituting value of x in terms of y in Eqn (2),

$\left(\frac{- 5 \cdot \left(2 y - 5\right)}{5}\right) + y = 3$

$- 2 y + 5 + y = 3$

$- 2 y + y = 3 - 5$

color(indigo)(y = 2

Substituting value of y in Eqn (1),

$5 x - 4 = - 5$

color(indigo)(x = -1/5