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

1 Answer
Jun 20, 2015

Answer:

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.