# How do you solve the system x-4y=27 and 3x+y=-23 using substitution?

Sep 11, 2016

$x = - 5$ and $y = - 8$

#### Explanation:

We have: $x - 4 y = 27$ and $3 x + y = - 23$

Let's solve the first equation for $x$:

$\implies x = 27 + 4 y$

Now, let's substitute this expression for $x$ into the second equation:

$\implies 3 \left(27 + 4 y\right) + y = - 23$

$\implies 81 + 12 y + y = - 23$

$\implies 13 y = - 104$

$\implies y = - 8$

Now, let's substitute this value of $y$ into the expression for $x$:

$\implies x = 27 + 4 \left(- 8\right)$

$\implies x = 27 - 32$

$\implies x = - 5$

Therefore, the solutions to the system of equations are $x = - 5$ and $y = - 8$.