SOLUTION: how do you solve this equation: 4x-8=4y, 4y+8=4x using the addition method.

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Question 1125261: how do you solve this equation: 4x-8=4y, 4y+8=4x using the addition method.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's the same equation twice.
No unique solution by any method.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given system:
4x-8=4y ....eq.1
4y%2B8=4x....eq.2
-------------------- ----simplify, both sides in both equations divide by 4
x-2=y ....eq.1
y%2B2=x....eq.2..->........solve or y
--------------------------
x-2=y ....eq.1
x-2=y....eq.2->........multiply by -1
---------------------------

x-2=y ....eq.1
-x%2B2=-y....eq.2
----------------------------add both eq.1 and eq.2
x-2%2B%28-x%2B2%29=y%2B%28-y%29
x-2-x%2B2=y-y
0=0

So we're left with 0=0 which means any x or y value will satisfy the system of equations. So there are an infinite number of solutions (we have coplanar lines, two lines that lie exactly on top of each other, actually it's same line), and this system is dependent.