of linear combination, the solution set of the system \( \left\{\begin{array}{l}3(2 x-3 y)=-2 \\ 5-15 y=-10 x\end{array}\right. \)

To find the solution set of the system of linear equations, we need to solve the system of equations. Given system of equations: \[ \left\{\begin{array}{l}3(2 x-3 y)=-2 \\ 5-15 y=-10 x\end{array}\right. \] Let's solve the system of equations step by step. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3\left(2x-3y\right)=-2\\5-15y=-10x\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}3\left(2x-3y\right)=-2\\x=\frac{-1+3y}{2}\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3\left(2\times \frac{-1+3y}{2}-3y\right)=-2\) - step3: Simplify: \(-3=-2\) - step4: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\) - step5: Rewrite: \((x, y) \in \varnothing\) The solution set of the system of linear equations is empty, which means there is no solution to the system of equations.