# What is the solution to the system of equations: 6=-4x+y, -5x-y=21?

##### 1 Answer
Nov 23, 2016

$x = - 3$ and $y = - 6$

#### Explanation:

1. $6 = - 4 x + y$
2. $- 5 x - y = 21$

From the first equation we can determine a value for $y$.

$6 = - 4 x + y$

Add $4 x$ to both sides.

$4 x + 6 = y$

In the second equation, substitute $y$ with $\textcolor{red}{\left(4 x + 6\right)}$.

$- 5 x - \textcolor{red}{\left(4 x + 6\right)} = 21$

Open the brackets and simplify. The multiplication of a negative and a positive results in a negative.

$- 5 x - \textcolor{red}{4 x - 6} = 21$

$- 9 x - 6 = 21$

Add $6$ to both sides.

$- 9 x = 27$

Divide both sides by $9$.

$- x = 3$ or $x = - 3$

In the first equation, substitute $x$ with $- 3$.

$6 = - 4 \left(- 3\right) + y$

Open the brackets. The multiplication of two negatives results in a positive.

$6 = 12 + y$

Subtract $12$ from both sides.

$- 6 = y$ or $y = - 6$