If you are expecting a number as the answer to x+y=? then you will have to think about the question again. For example:
- if x = 2 and y = -1 then 5x + 4y = 6 and x + y = 1 but
- if x = 6 and y = -6 then 5x + 4y = 6 and x + y = 0
5x+4y=6 means that the values of x and y depend on each other. If you were to draw a graph of this relationship, you would find that it is a line. For any specific value of x, there is a corresponding value of y, and for any specific value of y, there is a corresponding value of x.
So when you ask "what is x+y=?" you can now understand that x and y cannot be just chosen independently and still obey the relationship 5x+4y=6.
The best you can do is to solve the first equation for y:
5x + 4y = 6
4y = 6 - 5x
y = ( 6 - 5x ) / 4
Now you can replace the y in x+y=? with what y is equal to:
x + y
= x + (6 - 5x) / 4
= 4x / 4 + (6 - 5x) / 4
= (4x + 6 - 5x) / 4
= ( 6 - x ) / 4
So x + y = (6 - x) / 4.
Stephen and Penny