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

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

$\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.