Question

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

Answer 1

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:
`2x + y = 1`
`y = 1 - 2x`
Then you plug this value in `y` in the second equation:
`4x + 2(1-2x) = -1`
`4x + 2 - 4x = -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*(2x + y) = 2*(1)`
`4x + 2y = 2`

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