SOLUTION: In the problem 5.5x -1.5y =3.5 that I tried to solve for my niece. Since there were two variables and only one equation, I thought it can`t be solved but can be simplified only. S

Question 172259: In the problem 5.5x -1.5y =3.5 that I tried to solve for my niece.
Since there were two variables and only one equation, I thought it can`t be solved but can be simplified only. So I ended up with: 2x - 1.5y=0 . But she came home with x=3, y= 4 .
this confuses me:
how did you isolate y?
2 x - 1.5 y = 0

how did Y ended up on the other side of the equation

how did you get ( 2-1.5 ) x When 1.5 has no variable
Why is :
If 2x - 1.5y = 0
then y = (2/1.5)x = (4/3)x
or the same statement is
3y = 4x
--------------
_how did you get 3 & 4 ??????????? _ thanks

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Interesting!
First, if you were to substitute the answers brought home by your niece, you would quickly see that they do not work in the given equation:
Substituting x = 3 and y = 4, you get:
Simplifying...

Second, in your attempt to simplify the given equation, you cannot subtract 3.5 (a constant term) from 5.5x (a variable term) to get 2x. Why, that's like trying to subtract 3 pesos from 5 dollars...it can't be done directly!
Is it possible that your niece inadvertantly dropped the other equation on her way home from school?
Now there is a class of equations in which you have more unknowns than you have equations, and these are called Diophantine equations. But their solutions depend on certain restrictions placed on the variables, e.g. they must be integers.
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