If $3x+2y=7$ and $4x-y=24$, then find the value of $x-y$.

We are given a system of two linear equations:$3x+2y=7$$4x-y=24$ Multiply equation (2) by 2 to match the coefficients of $y$:
$$2\times (4x-y)=2\times 24⟹8x-2y=48\text{— (3)}$$
Add equation (1) and equation (3):
$$(3x+2y)+(8x-2y)=7+48$$
$$11x=55$$
$$x=5$$
Substitute $x=5$ back into equation (2):
$$4(5)-y=24$$
$$20-y=24$$
$$y=20-24=-4$$
Now evaluate the required expression $x-y$:
$$x-y=5-(-4)=5+4=9$$