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Question 797005: I have two Questions. My first one is, How do you algebraically figure out if vales of x and y can be the same?
For example, In this equation 12= 2x + 3y I can figure out through guess and check that the number 2.4 can be used for x and y at the same time.
Now for my next question.
Say you have something like this:
24= 4x + 8y
How do I determine algebraically what values of y and x will make 24 equal to 0?
Thanks so much!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
If  , then I can substitute  for  and re-write the equation as
 -->  -->  --> 
If  , and are related by that equation, and we can find some of the infinite pairs of values (x,y) that satisfy that equation.
(Finding infinite pairs would take infinite time, and I only have a few minutes until my bedtime).
24 will never be 0, or anything other than 24.
However, maybe you are thinking of finding what value of x corresponds to  for that equation, and what value of y corresponds to  for that equation.
--> --> --> --> -->
So the pair (0,3), with and satisfies the relation
--> --> --> --> -->
So the pair (6,0), with and satisfies the relation
Those two data pairs, and the infinite pairs (x,y) that satisfy can be graphed as
 Equations like and are called linear equations and their graphs are straight line.
If an equation has an x, and/or a y, and the x and/or y are at most multiplied times numbers and added or subtracted (no exponents, no x or y in a denominator, no other fancy stuff), it is a linear equation.
 ,  , and  are linear equations 
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