# How do you solve x+4y=-1, -3x-14=y by substitution?

## List item

Dec 7, 2016

$x = - 5$ and $y = 1$

#### Explanation:

$x + 4 y = - 1$
$- 3 x - 14 = y$

From the second equation, we know the value of $y$ as $\textcolor{red}{\left(- 3 x - 14\right)}$. So in the first equation, substitute $y$ with $\textcolor{red}{\left(- 3 x - 14\right)}$.

$x + 4 y = - 1$

$x + 4 \textcolor{red}{\left(- 3 x - 14\right)} = - 1$

Open the brackets and simplify. The product of positive and negative is a negative.

$x - 12 x - 56 = - 1$

$- 11 x - 56 = - 1$

Add $56$ to both sides.

$- 11 x = 55$

Divide both sides by $11$.

$- x = 5$ or $x = - 5$

In the first equation, substitute $x$ with $\textcolor{b l u e}{- 5}$.

$x + 4 y = - 1$

$\textcolor{b l u e}{- 5} + 4 y = - 1$

Add $5$ to both sides.

$4 y = 4$

Divide both sides by $4$.

$y = 1$