To solve the given system of equations using Cramer's Rule, we follow these steps:
1. Write down the system of equations:
[tex]\[
\begin{array}{l}
-x - 3y = -3 \\
-2x - 5y = -8
\end{array}
\][/tex]
2. Define the coefficient matrix [tex]\( A \)[/tex] and the constants matrix [tex]\( B \)[/tex]:
[tex]\[
A = \begin{bmatrix}
-1 & -3 \\
-2 & -5
\end{bmatrix}
\quad \text{and} \quad
B = \begin{bmatrix}
-3 \\
-8
\end{bmatrix}
\][/tex]
3. Calculate the determinant of the coefficient matrix [tex]\( A \)[/tex]:
[tex]\[
\text{det}(A) = (-1 \cdot -5) - (-3 \cdot -2) = 5 - 6 = -1
\][/tex]
4. Form the matrix [tex]\( A_1 \)[/tex] by replacing the first column of [tex]\( A \)[/tex] with matrix [tex]\( B \)[/tex]:
[tex]\[
A_1 = \begin{bmatrix}
-3 & -3 \\
-8 & -5
\end{bmatrix}
\][/tex]
5. Calculate the determinant of the matrix [tex]\( A_1 \)[/tex]:
[tex]\[
\text{det}(A_1) = (-3 \cdot -5) - (-3 \cdot -8) = 15 - 24 = -9
\][/tex]
6. According to Cramer's Rule, the value of [tex]\( x \)[/tex] is given by:
[tex]\[
x = \frac{\text{det}(A_1)}{\text{det}(A)} = \frac{-9}{-1} = 9
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] in the solution to the system of equations is [tex]\( x = 9 \)[/tex].
