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 \(8 = k * 4\). 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 \[y = 5*3.23 - 15 = 1.15\]

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