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Math Help - Point of intersection

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    56

    Point of intersection

    Problem: Find the point of intersection of the lines x_1-5x_2=1 and 3x_1-7x_2=5.

    Solve the system using elementary row operations on the equations or on the augmented matrix.
    ________________

    I'm doing something wrong here, and I don't know what. Can someone help?

    R1 = row 1
    R2 = row 2

    <br />
\begin{bmatrix}<br />
1 & -5 & 1\\ <br />
3 & -7 & 5\\<br />
\end{bmatrix}<br />

    -3*R1 + R2
    <br />
\begin{bmatrix}<br />
1 & -5 & 1\\ <br />
0 & 8 & 2\\<br />
\end{bmatrix}<br />

    (1/8)*R2
    <br />
 \begin{bmatrix}<br />
 1 & -5 & 1\\ <br />
 0 & 1 & \frac{1}{4}\\<br />
 \end{bmatrix}<br />

    5*R2 +R1
    <br />
 \begin{bmatrix}<br />
 1 & 0 & \frac{5}{4}\\ <br />
 0 & 1 & \frac{1}{4}\\<br />
 \end{bmatrix}<br />

    I get x_1=\frac{5}{4} and x_2=\frac{1}{4}, but plugging them into the 1st equation doesn't work.
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  2. #2
    MHF Contributor

    Joined
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    \frac{5}{4}+ 1= \frac{9}{4}, not \frac{5}{4}.
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