Question

Solve the given augmented matrix: (1 point)
-3 1 4
5 3 12

no solution
no solution

(-2, 3)
(-2, 3)

(3, 6)
(3, 6)

(0, 4)
(0, 4)

Answer 1

To solve the augmented matrix:

\[
\begin{bmatrix}
-3 & 1 & | & 4 \\
5 & 3 & | & 12
\end{bmatrix}
\]

We can represent the equations based on the matrix:

1. \(-3x + y = 4\)
2. \(5x + 3y = 12\)

Let's solve this system of equations.

### Step 1: Solve for \(y\) in the first equation
From the first equation, we can express \(y\) in terms of \(x\):

\[
y = 4 + 3x
\]

### Step 2: Substitute \(y\) into the second equation
Now we substitute this expression for \(y\) into the second equation:

\[
5x + 3(4 + 3x) = 12
\]

### Step 3: Simplify and solve for \(x\)
Expanding and simplifying:

\[
5x + 12 + 9x = 12
\]

\[
14x + 12 = 12
\]

Subtracting 12 from both sides:

\[
14x = 0
\]

Dividing by 14 gives:

\[
x = 0
\]

### Step 4: Back substitute to find \(y\)
Now we substitute \(x = 0\) back into the equation for \(y\):

\[
y = 4 + 3(0) = 4
\]

### Solution
The solution to the system is:

\[
(x, y) = (0, 4)
\]

Therefore, the final answer is:

\((0, 4)\)