Solve for variable x:
4)
\[
\begin{array}{l}
-6 x+9 y=15 \\
6 x+3 y=21
\end{array}
\]

Step 1 ：Multiply the first equation by 2 and the second equation by -1: \(\begin{cases} -12x + 18y = 30 \\ 6x + 3y = 21 \end{cases}\)

Step 2 ：Add the two equations together: \((-12x + 18y) + (6x + 3y) = 30 + 21\)

Step 3 ：Simplify the equation: \(-6x + 21y = 51\)

Step 4 ：Divide both sides of the equation by 3: \(\frac{-6x}{3} + \frac{21y}{3} = \frac{51}{3}\)

Step 5 ：Simplify the equation: \(-2x + 7y = 17\)

Step 6 ：Substitute the value of \(-2x + 7y\) from the second equation into the first equation: \(-2x + 7(3 - 2x) = 17\)

Step 7 ：Simplify the equation: \(-2x + 21 - 14x = 17\)

Step 8 ：Combine like terms: \(-16x + 21 = 17\)

Step 9 ：Subtract 21 from both sides of the equation: \(-16x = -4\)

Step 10 ：Divide both sides of the equation by -16: \(x = \frac{-4}{-16}\)

Step 11 ：Simplify the equation: \(x = \frac{1}{4}\)