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

Jun 20, 2015

You can't since this system doesn't have a solution.

#### Explanation:

Method 1
You can see this by trying subsitution.
First you seperate the $y$ variable in the first equation:
$2 x + y = 1$
$y = 1 - 2 x$
Then you plug this value in $y$ in the second equation:
$4 x + 2 \left(1 - 2 x\right) = - 1$
$4 x + 2 - 4 x = - 1$
$2 = - 1$

2 equals -1??? That doesn't seem right. Since all our previous steps are correct, we can conclude that this system doesn't have a solution.

Method 2
You could have also seen this quicker, by multiplying the first equation by two (which is allowed).

$2 \cdot \left(2 x + y\right) = 2 \cdot \left(1\right)$
$4 x + 2 y = 2$

But the second equation says that $4 x + 2 y = - 1$. There must be something wrong here, so the system doesn't have a solution.