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Math Help - solving equations

  1. #1
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    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.

    <br />
\begin{array}{l}<br />
 B_1  = \frac{{1.5H_1 }}{{100 + H_1 }} \\ <br />
 B_2  = \frac{{1.5H_2 }}{{100 + H_2 }} \\ <br />
 1000 = H_1  \times 0.25 + H_2  \times 0.5 \\ <br />
 \left( {25 \times 10^{ - 4} } \right)B_1  = (12.5 \times 10^{ - 4} )B_2  \\ <br />
 \end{array}<br />
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  2. #2
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    Quote Originally Posted by Craka View Post
    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.

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