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

1 Answer
Nico Ekkart
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:
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.

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