I suspect this is a ratter dumb question, but I just want to be sure. I need to find W in the following equation: $$W=\frac{3}{2}x+\frac{6}{5}y+\frac{2}{7}z$$ And the only thing I know is: $$5=3x+6y+2z$$
Of course this a simplification of the real problem, but is it possible to find W?
Thank you!
On
Unfortunately, you have what's called an undetermined system - since you have 2 equations with 4 unknown variables you cannot find a single solution to $W$.
What you can do is remove one of the variables by solving for that variable in the second equation and substituting it into the first equation:
$$ x=\frac{5}{3}-2y-\frac{2}{3}z \\ W=\frac{3}{2}\left(\frac{5}{3}-2y-\frac{2}{3}z\right)+\frac{6}{5}y+\frac{2}{7}z= \frac{5}{2}-\frac{9}{5}y-\frac{5}{7}z $$
Here, your solution to $W$ is more like a function of two variables, $y$ and $z$, so if you can get values for $y$ and $z$ or get two more equations, then you can solve for $W$.
Well, for example the second equation is satisfied by both $$(x,y,z)=(1,1,-2)$$ and $$(x,y,z)=(0,1,-\frac{1}{2})$$ but both yield different results for $W$. So you need more information to find $W$. Does this make it clearer?