Given the simultaneous linear equations $2x-3y=-12$ and $\frac{x}{y}=\frac{3}{4}$, what are the values of $x$ and $y$?

Let's solve the equations step-by-step:
From the second equation, we have:

$$\frac{x}{y}=\frac{3}{4}⟹x=\frac{3}{4}y$$

Substitute this expression for $x$ into the first equation:

$$2\left(\frac{3}{4}y\right)-3y=-12$$

$$\frac{3}{2}y-3y=-12$$

Take the common denominator:

$$\frac{3y-6y}{2}=-12$$

$$\frac{-3y}{2}=-12$$

$$-3y=-24⟹y=8$$

Now, substitute the value of $y$ back to find $x$:

$$x=\frac{3}{4}(8)=3\times 2=6$$

Thus, the unique solution is $x=6$ and $y=8$.