Solving for multiple unknown variables Assume for this scenario that:
a = b * c 
d = b - c
I only know the value for a and d (in this case 0.075 and 239, respectively), and I need to solve for both b and c. Is this possible to solve given the limited information, and if so what is the best approach to do so?
 A: This is known as a system of nonlinear simultaneous equations. In this case, it is very easy to solve the system.
First, write $b$ in terms of $d$ and $c$, where $d$ is known:
$$b = d+c.$$
Substitute this into the first equation:
$$a = bc = (d+c)c = cd+c^2$$
Solve this for $c$ using the quadratic formula:
$$ c^2+dc-a = 0 \implies c = -\frac{d}{2}\pm \frac{\sqrt{d^2+4a}}{2}$$
Substitute the solutions back into the equation $b = d+c$ to find values of $b$.
A: Yes, there is a solution. I recommend checking the exact form (not approximate) as provided by wolfram alpha.
Solution
This supports Ed's answer
A: Rewrite your two equations:
$$
\begin{cases}
.075 = b\times c \\ 239 = b-c
\end{cases}
$$
Now solve the second equation for $b$ so that $b=239+c$. Plug this into the first equation in place of $b$:
$$
.075 = (239+c)\times c
$$
Do you know how to solve quadratic equations? Once you have the possible values of $c$, plug those back into our equation for $b$ to get the final answer. This method is called eliminating a variable by substitution.
