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Math Help - Answers vary with Cramer's Rule...Why?

  1. #1
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    Answers vary with Cramer's Rule...Why?

    Hello -

    I have solved the following for x1 and x2 with z = 0.005 for b1=1 and b2=3. then again for b1=1.1 and b2=3. The answers vary by quite a bit for such a small change (0.5 to -2.495). can anyone tell me why this would be? thanks!

    <br />
\begin{bmatrix}<br />
1+3z & 1-3z \\<br />
3-z & 3+z \end{bmatrix}<br />
\begin{bmatrix}<br />
x1 \\<br />
x2 \end{bmatrix}<br />
=<br />
\begin{bmatrix}<br />
b1 \\<br />
b2 \end{bmatrix}<br />
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  2. #2
    Super Member
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    When you solve a pair of equations like these, you are, from the geometrical point of view, finding the co-ordinates of the point of intersection of two straight lines.
    If the lines are very nearly parallel, as these are, a very small change in the slope of either of the lines can cause a large movement in the point of intersection and hence a large movement in the solution of the two equations.
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