https://r2.erweima.ai/mathbot/image/172564393684705if7yym.jpg

Alguien podría decirme de dónde rayos salió ese 6 en el primer ejercicio porfi ❤️ para saber cómo sacar el del 2do ejercicio

The image you uploaded seems to contain a solution for a system of equations using determinants, specifically Cramer's rule.

Let's break down how the number \(6\) was derived in the first exercise:

### Cramer's Rule Overview:
Cramer's rule solves systems of linear equations using determinants. For a system of equations:
\[
\begin{aligned}
ax + by &= e \\
cx + dy &= f
\end{aligned}
\]
You solve for \(x\) and \(y\) using determinants. For example, to solve for \(x\):
\[
x = \frac{\Delta_x}{\Delta}
\]
Where:
- \(\Delta\) is the determinant of the coefficient matrix.
- \(\Delta_x\) is the determinant of the matrix formed by replacing the \(x\)-column with the constants from the right-hand side of the equations.

### Analyzing the First Problem:

It seems to be solving this system:
\[
\begin{aligned}
x + 4y &= 11 \\
3x + 5y &= 13
\end{aligned}
\]

1. **Step 1: Find \(\Delta\)** (the determinant of the coefficient matrix):
   The coefficient matrix is:
   \[
   \begin{pmatrix}
   1 & 4 \\
   3 & 5
   \end{pmatrix}
   \]
   The determinant \(\Delta\) is:
   \[
   \Delta = (1 \times 5) - (4 \times 3) = 5 - 12 = -7
   \]

2. **Step 2: Find \(\Delta_x\)** (replace the \(x\)-column with the constants):
   The new matrix is:
   \[
   \begin{pmatrix}
   11 & 4 \\
   13 & 5
   \end{pmatrix}
   \]
   The determinant \(\Delta_x\) is:
   \[
   \Delta_x = (11 \times 5) - (13 \times 4) = 55 - 52 = 3
   \]

3. **Step 3: Solve for \(x\)**:
   \[
   x

Understand how to solve a system of linear equations using Cramer's Rule. Learn the steps to calculate determinants and find the values for x and y. This solution walks through the process with detailed explanations, making it suitable for students in Grades 10-12.

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