system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible to find four different numbers a, b, c, d that a*b=c*d and a+b=c+d?
gpt
No, and you can prove it yourself!  Start by solving one equation for one of the variables, then substitute it into the second equation.  Here are the full steps, but maybe it would be best to try to work further on your own after reading one before reading the next.

First, if any of a, b, c, or d is 0, then another one must be 0.  Why?  So, if we want different numbers, none of them can be 0.  Let's assume this is the case.

Start by solving the first equation for a: a = cd/b.

Then the second equation becomes cd/b + b = c + d.

Move everything to one side: b + cd/b - c - d = 0.

Multiply through by b: b^2 - b(c+d) + cd = 0.

Factor: (b-c)(b-d) = 0.

What does this tell you?