What is the solution to the system of equations x = y - 1 and 2x + y = -2?

Dec 28, 2015

$x = - 1$ and $y = 0$

Explanation:

$\textcolor{w h i t e}{\times} x = y - 1$, $2 x + y = - 2$

$\textcolor{w h i t e}{\times} 2 x + y = - 2 \iff x = \frac{- y - 2}{2}$

$\implies y - 1 = \frac{- y - 2}{2}$
$\implies \textcolor{red}{2 \times} \left(y - 1\right) = \textcolor{red}{2 \times} \frac{- y - 2}{2}$
$\implies 2 y - 2 \textcolor{red}{+ 2} = - y - 2 \textcolor{red}{+ 2}$
$\implies y = 0$

$\textcolor{w h i t e}{\times} x = y - 1$
$\textcolor{w h i t e}{\times x} = \textcolor{b l u e}{0} - 1$
$\textcolor{w h i t e}{\times x} = - 1$