Given the direct variation equation $y=kx$, where $y=8$ when $x=4$, and a system of equations where $2x+3y=10$ and $5x-y=15$, find the value of $k$ and the solutions to the system of equations.

Step 1 ：Step 1: Find the value of $k$ in the direct variation equation. Since $y=kx$, we can substitute $y=8$ and $x=4$ to get $8=k\ast 4$. Solving for $k$ gives us $k=2$.

Step 2 ：Step 2: Solve the system of equations. We can use the substitution or elimination method. Let's use the substitution method. From the second equation $5x-y=15$, we can express $y$ in terms of $x$: $$y=5x-15$$ Substituting this into the first equation gives: $$2x+3(5x-15)=10$$ Simplifying gives us $$2x+15x-45=10$$ $$17x=55$$ $$x=\frac{55}{17}=3.23$$ Substituting $x=3.23$ into the equation $y=5x-15$ gives us $$y=5\ast 3.23-15=1.15$$

Step 3 ：So the solutions to the system of equations are $x=3.23$ and $y=1.15$