Question

Solve the system using an augmented matrix. Show all work.

{−x−3y=−17
2x−6y=−26

Answer 1

The system of equations can be represented as an augmented matrix:

\[
\begin{array}{ccc|c}
-1 & -3 & -17 \\
2 & -6 & -26 \\
\end{array}
\]

To solve the system using row operations, we will first perform row operations to get a leading 1 in the first column and zeros below it.

\[
\begin{array}{ccc|c}
-1 & -3 & -17 \\
2 & -6 & -26 \\
\end{array}
\]

Multiply the first row by -2 and add it to the second row:

\[
\begin{array}{ccc|c}
-1 & -3 & -17 \\
0 & 0 & 8 \\
\end{array}
\]

This means the second row represents the equation 0x + 0y = 8, which simplifies to 0 = 8. Since this equation is not true, the system has no solution.

Therefore, the system is inconsistent and there is no solution.