Solve for y in 2x + y = 1 and x - 2y =-7?

Apr 7, 2015

If $2 x + y = 1$
then
$4 x + 2 y = 2$

We can add the second equation to this to eliminate the $y$ term

$\left(\begin{matrix}\null & 4 x & + & 2 y & = & 2 \\ + & x & - & 2 y & = & - 7 \\ \null & 5 x & \null & \null & = & - 5\end{matrix}\right)$

$\rightarrow x = - 1$

Substituting $x = - 1$ back into the original first equation we get
$2 \left(- 1\right) + y = 1$
which simplifies as
$y = 3$