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Thread: Point of intersection

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    56

    Point of intersection

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

    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

    $\displaystyle
    \begin{bmatrix}
    1 & -5 & 1\\
    3 & -7 & 5\\
    \end{bmatrix}
    $

    -3*R1 + R2
    $\displaystyle
    \begin{bmatrix}
    1 & -5 & 1\\
    0 & 8 & 2\\
    \end{bmatrix}
    $

    (1/8)*R2
    $\displaystyle
    \begin{bmatrix}
    1 & -5 & 1\\
    0 & 1 & \frac{1}{4}\\
    \end{bmatrix}
    $

    5*R2 +R1
    $\displaystyle
    \begin{bmatrix}
    1 & 0 & \frac{5}{4}\\
    0 & 1 & \frac{1}{4}\\
    \end{bmatrix}
    $

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

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