Point of intersection

**Cursed** · May 19th 2010, 08:13 AM

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

R1 = row 1
R2 = row 2

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

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

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

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

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

**HallsofIvy** · May 19th 2010, 08:57 AM

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

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