1. ## solving equations

I'm trying to solve the following set of equations, I'm trying to work out how to put them into matrix form to solve, but I can't see how to.

$\displaystyle \begin{array}{l} B_1 = \frac{{1.5H_1 }}{{100 + H_1 }} \\ B_2 = \frac{{1.5H_2 }}{{100 + H_2 }} \\ 1000 = H_1 \times 0.25 + H_2 \times 0.5 \\ \left( {25 \times 10^{ - 4} } \right)B_1 = (12.5 \times 10^{ - 4} )B_2 \\ \end{array}$

2. Originally Posted by Craka
I'm trying to solve the following set of equations, I'm trying to work out how to put them into matrix form to solve, but I can't see how to.

$\displaystyle \begin{array}{l} B_1 = \frac{{1.5H_1 }}{{100 + H_1 }} \\ B_2 = \frac{{1.5H_2 }}{{100 + H_2 }} \\ 1000 = H_1 \times 0.25 + H_2 \times 0.5 \\ \left( {25 \times 10^{ - 4} } \right)B_1 = (12.5 \times 10^{ - 4} )B_2 \\ \end{array}$
You can't put them into matrix form because they are not linear equations.

But you can do a lot to simplify them. For start, the last equation just says that $\displaystyle B_2=2B_1$. So it follows from the first two equations that $\displaystyle \frac{H_2}{100+H_2} = \frac{2H_1}{100+H_1}$. Multiply out those fractions, substitute $\displaystyle H_1 = 4000 - 2H_2$ (from the third equation), and you'll have a quadratic equation for $\displaystyle H_2$. Once you know $\displaystyle H_2$, you can substitute back and find the other unknowns quite easily.