Solve the system of equation:
\[
\left\{\begin{array}{l}
-16 y=4 x \\
4 x+27 y=11
\end{array}\right.
\]

Step 1 ：Understand the problem: We are given a system of two equations with two variables, x and y. We need to find the values of x and y that satisfy both equations simultaneously.

Step 2 ：Solve the first equation for x: The first equation is -16y = 4x. We can solve this equation for x by dividing both sides by 4, which gives us \(x = -4y\).

Step 3 ：Substitute x into the second equation: Now we can substitute \(x = -4y\) into the second equation, which gives us \(4(-4y) + 27y = 11\), simplifying this gives us \(11y = 11\).

Step 4 ：Solve for y: Divide both sides by 11 to solve for y, which gives us \(y = 1\).

Step 5 ：Substitute y into the first equation: Now we can substitute \(y = 1\) into the first equation to solve for x, which gives us \(-16(1) = 4x\), simplifying this gives us \(-16 = 4x\).

Step 6 ：Solve for x: Divide both sides by 4 to solve for x, which gives us \(x = -4\).

Step 7 ：Check the solution: Substitute \(x = -4\) and \(y = 1\) into both original equations to check if they are true. For the first equation, \(-16(1) = 4(-4)\) simplifies to \(-16 = -16\) which is true. For the second equation, \(4(-4) + 27(1) = 11\) simplifies to \(11 = 11\) which is also true.

Step 8 ：So, the solution to the system of equations is \(\boxed{x = -4}\) and \(\boxed{y = 1}\).