1. ## 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.
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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.

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