help! i don't know what this is!
- Thread starter jamesbee
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What does that even mean?jamesbee said:
Generally, one must assume y = f(x) or x = f(y). This notation means it is "solved for" one variable or the other. To "solve for" both would seem to indicate x = y, which may not be all that interesting.
You can solve for either x or y as you wish. I get y = 2x - 3 for x <> 4 or x = ½(y+3) for y <> 5
Whoever told you to split it up like that, are they also trying to sell you a used car? Run screaming.
There is not a unique x and not a unique y for the solution set.
There are infinite numbers of (x, y) solutions.
2 = (5 - y)/(4 - x)
For instance, this can be:
\(\displaystyle \frac{2}{1} = \frac{5 - y}{4 - x}\)
\(\displaystyle 2 = 5 - y\) and \(\displaystyle 1 = 4 - x\) . . . The solution here is \(\displaystyle (3, 3).\)
Or, it can be:
\(\displaystyle \frac{-2}{-1} = \frac{5 - y}{4 - x}\)
\(\displaystyle -2 = 5 - y\) and \(\displaystyle -1 = 4 - x\) . . . The solution here is \(\displaystyle (5 ,7).\)
Or, it can be:
\(\displaystyle \frac{4}{2} = \frac{5 - y}{4 - x}\)
\(\displaystyle 4 = 5 - y\) and \(\displaystyle 2 = 4 - x\) . . . The solution here is \(\displaystyle (2, 1).\)
Or, it can be one of an infinite number of solutions.
It cannot be split up in that way that you were told.
There are infinite numbers of (x, y) solutions.
2 = (5 - y)/(4 - x)
For instance, this can be:
\(\displaystyle \frac{2}{1} = \frac{5 - y}{4 - x}\)
\(\displaystyle 2 = 5 - y\) and \(\displaystyle 1 = 4 - x\) . . . The solution here is \(\displaystyle (3, 3).\)
Or, it can be:
\(\displaystyle \frac{-2}{-1} = \frac{5 - y}{4 - x}\)
\(\displaystyle -2 = 5 - y\) and \(\displaystyle -1 = 4 - x\) . . . The solution here is \(\displaystyle (5 ,7).\)
Or, it can be:
\(\displaystyle \frac{4}{2} = \frac{5 - y}{4 - x}\)
\(\displaystyle 4 = 5 - y\) and \(\displaystyle 2 = 4 - x\) . . . The solution here is \(\displaystyle (2, 1).\)
Or, it can be one of an infinite number of solutions.
It cannot be split up in that way that you were told.