$\left\{\begin{array}{c}10 x-3 y=18 \\ -2 x+3 y=6\end{array}\right.$

Step 1 ：Given the system of equations: \(\begin{cases} 10x - 3y = 18 \\ -2x + 3y = 6 \end{cases}\)

Step 2 ：We can solve this system by elimination. By adding the two equations, we can eliminate y.

Step 3 ：Adding the two equations gives us: \(10x - 3y - 2x + 3y = 18 + 6\)

Step 4 ：Simplifying the equation gives us: \(8x = 24\)

Step 5 ：Dividing both sides by 8, we find that \(x = 3\)

Step 6 ：Substituting \(x = 3\) into the first equation, we get: \(10*3 - 3y = 18\)

Step 7 ：Solving for y, we find that \(y = 4\)

Step 8 ：The solution to the system of equations is \(\boxed{x = 3, y = 4}\)