SOLUTION: Do the equations x = 5y + 3 and x = 5y � 3 have the same solution? How might you explain your answer to someone who has not learned algebra?

Question 671826: Do the equations x = 5y + 3 and x = 5y � 3 have the same solution? How might you explain your answer to someone who has not learned algebra?
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let's say that you have two big sacks that each have the same number of things in them. Take 3 of the things out of one bag and then put them into the other bag. Is it possible for the two bags to STILL contain the same number of things?

John

My calculator said it, I believe it, that settles it

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
No, the equations x = 5y + 3 and x = 5y � 3 do NOT have the same solution because this system is inconsistent (and therefore, there are no solutions at all).

A way to explain it to someone who has not learned algebra:

y is some number. So 5 times y (5y) is some (different) number as well.

This means that

x = 5y + 3

is the same as

x = Some Number + 3

and

x = 5y - 3

is the same as

x = Some Number - 3

But we have a problem. x can only be ONE number at a time; however, the statements "some number + 3" and "some number - 3" yield different numbers every time (for any number that replaces "some number"). Go ahead and try it out with a few numbers.

So we get a contradiction which leads to no solutions.
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