Question

Solve the augmented matrix below.
4 2 10
1 -1 13
x= y=

Answer 1

To solve the given augmented matrix, we will first rewrite it in a more standard form:

\[
\begin{bmatrix}
4 & 2 & | & 10 \\
1 & -1 & | & 13
\end{bmatrix}
\]

This represents the system of equations:
1. \( 4x + 2y = 10 \)
2. \( x - y = 13 \)

We will solve this system step by step.

### Step 1: Solve for one variable
From the second equation \( x - y = 13 \), we can express \( x \) in terms of \( y \):
\[
x = y + 13
\]

### Step 2: Substitute into the first equation
Now, we can substitute \( x \) into the first equation:
\[
4(y + 13) + 2y = 10
\]
Expanding this:
\[
4y + 52 + 2y = 10
\]
Combine like terms:
\[
6y + 52 = 10
\]
Now, isolate \( y \):
\[
6y = 10 - 52
\]
\[
6y = -42
\]
\[
y = -7
\]

### Step 3: Substitute back to find \( x \)
Now that we have \( y \), we can substitute it back into the equation for \( x \):
\[
x = y + 13
\]
\[
x = -7 + 13
\]
\[
x = 6
\]

### Final Solution
Thus, the solution to the system is:
\[
x = 6
\]
\[
y = -7
\]

So, in conclusion:
\[
x = 6, \quad y = -7
\]