Point of intersection

Sep 2007
56
5
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.
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
\(\displaystyle \frac{5}{4}+ 1= \frac{9}{4}\), not \(\displaystyle \frac{5}{4}\).