Question

Solve the augmented matrix below
1 -1 3
7 -1 -3

Answer 1

To solve the augmented matrix corresponding to the system of equations, let's rewrite the augmented matrix in standard form:

\[
\begin{bmatrix}
1 & -1 & | & 3 \\
7 & -1 & | & -3
\end{bmatrix}
\]

This matrix corresponds to the following system of linear equations:

1. \(x - y = 3\)
2. \(7x - y = -3\)

We can solve this system using the method of elimination or substitution. I'll use elimination.

### Step 1: Eliminate \(y\)

We can subtract the first equation from the second to eliminate \(y\):

\[
(7x - y) - (x - y) = -3 - 3
\]

This simplifies to:

\[
6x = -6
\]

### Step 2: Solve for \(x\)

Dividing both sides by 6 gives:

\[
x = -1
\]

### Step 3: Substitute \(x\) back to find \(y\)

Now substitute \(x = -1\) into the first equation:

\[
-1 - y = 3
\]

This simplifies to:

\[
-y = 4 \quad \Rightarrow \quad y = -4
\]

### Conclusion

The solution to the system of equations represented by the augmented matrix is:

\[
x = -1, \quad y = -4
\]

Thus, the solution can be written as the ordered pair:

\[
(x, y) = (-1, -4)
\]