Use Cramer's rule to find the solution to the following system of linear equations.
\[
\begin{array}{l}
5 x+3 y=3 \\
x-2 y=6
\end{array}
\]

Step 1 ：Given the system of linear equations: \[ \begin{array}{l} 5x + 3y = 3 \ x - 2y = 6 \end{array} \]

Step 2 ：We will use Cramer's rule to find the solution. The formulas for Cramer's rule are: \(x = \frac{ed - bf}{ad - bc}\) and \(y = \frac{af - ec}{ad - bc}\)

Step 3 ：Substituting the coefficients and constants from our system of equations into these formulas, we get: \(x = \frac{3*(-2) - 3*6}{5*(-2) - 3*1}\) and \(y = \frac{5*6 - 3*1}{5*(-2) - 3*1}\)

Step 4 ：Solving these equations, we find that \(x = 1.8461538461538463\) and \(y = -2.076923076923077\)

Step 5 ：\(\boxed{The solution to the system of equations is \(x = 1.8461538461538463\) and \(y = -2.076923076923077\)}