SOLUTION: Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra?

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Question 625475: Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra?
Found 2 solutions by richwmiller, KMST:
Answer by richwmiller(9144) About Me  (Show Source):
You can put this solution on YOUR website!
I answered this question last week. They are two lines that never meet.
So they can't have the same solutions.

Answer by KMST(1936) About Me  (Show Source):
You can put this solution on YOUR website!
No matter what value y takes,
4y%2B1 is one more than 4y.
4y-1 is one less than 4y.
They are clearly two different numbers and
x cannot be two different numbers at the same time.

A different explanation would involve functions, graphs, geometry, triangles, and proportions. All of that is beautifully intuitive math that does not require algebra, but it is not customary to talk about that to people who have not learned algebra. (I see no good reason to introduce math concepts in one order or another, but it is hard to fight tradition).