# How do you solve the system x = −2y − 1 and 2x + y = −20?

May 27, 2015

Given
$\text{[1] } x = - 2 y - 1$
$\text{[2] } 2 x + y = - 20$

We can substitute for $x$ in [2] the expression for $x$ in [1]
$\text{[3] } 2 \left(- 2 y - 1\right) + y = - 20$
Simplifying
$\text{[4] } - 3 y - 2 = - 20$
which implies
[5] "y=6

Substituting the value for $y$ back into [1]
$\text{[6] } x = - 2 \left(6\right) - 1$
implying
$\text{[7] } x = - 13$

Solution is $\left(x , y\right) = \left(- 13 , 6\right)$