# How do you solve the system by substitution x – 4y = –19 and –4x – 5y = 13?

Apr 18, 2017

y=3

#### Explanation:

You can get "x" by itself in the first equation by adding "4y" to both sides of the equation:

$x - 4 y + 4 y = - 19 + 4 y$

This should leave you with:

$x = 4 y - 19$

Now you can substitute it into the second equation:

$- 4 \left(4 y - 19\right) - 5 y = 13$

Distribute the "-4" to the numbers in the parenthesis:

$- 16 y + 76 - 5 y = 13$

Combine like terms:

$- 21 y + 76 = 13$

Subtract 76 from both sides to get "y" by itself:

$- 21 y + 76 - 76 = 13 - 76$

Now divide both sides by "-21":

$\frac{- 21 y}{-} 21 = \frac{- 63}{-} 21$

You should end up with:

$y = \frac{- 63}{-} 21$

You can change it to a decimal by using a calculator:

y=3.