# How do you solve the following system?:  4x-5y=5 , 5y = x + 10

Apr 4, 2018

$x = 5$ and $y = 3$.

#### Explanation:

Easiest way to solve this is by substitution.

Equation 1: $4 x - 5 y = 5$

Equation 2: $5 y = x + 10$

Solve Equation 2 for $x$

$x = 5 y - 10$

Substitute this expression for $x$ into Equation 1.

$4 \left(5 y - 10\right) - 5 y = 5$

Apply the distributive property.

$20 y - 40 - 5 y = 5$

Combine like terms.

$15 y = 45$

$y = 3$

Substitute this value for $y$ into Equation 2.

$5 \cdot 3 = x + 10$

$x = 5$