# How do you solve the system 2x + y = 1  and 4x + 2y = −1 by substitution?

May 31, 2015

We have the following system :

$2 x + y = 1$
$4 x + 2 y = - 1$

We need to isolate $x$ or $y$ on one of the equations. Let's isolate $y$ on the first one, it's the easiest :

$2 x + y = 1 \Leftrightarrow y = 1 - 2 x$

Now we can replace the $y$ on the second equation :

$4 x + 2 y = 4 x + 2 \left(1 - 2 x\right) = 4 x - 4 x + 2 = 2 \ne - 1$.

There aren't any solutions to that system.