# solving equations

• Apr 7th 2009, 11:53 PM
Craka
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.

$
\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}
$
• Apr 8th 2009, 11:06 AM
Opalg
Quote:

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.

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