Solve for the variable x.: $\begin{array}{c}3 x-y=4 \\ 2 x-3 y=-9\end{array}$

Step 1 ：Given the system of equations: \(3x - y = 4\) and \(2x - 3y = -9\)

Step 2 ：Multiply the first equation by 3 and the second equation by 1 to make the coefficients of y the same in both equations: \(9x - 3y = 12\) and \(2x - 3y = -9\)

Step 3 ：Subtract the second equation from the first: \((9x - 2x) - (3y - 3y) = 12 - (-9)\)

Step 4 ：This simplifies to: \(7x = 21\)

Step 5 ：Solve for x by dividing both sides by 7: \(x = \frac{21}{7}\)

Step 6 ：\(\boxed{x = 3}\)