Find the direct variation equation of a system of equations where \(y = 3x + 2\) and \(y = 5x - 1\).

Step 1 ：Step 1: In a direct variation, the equation can be written in the form \(y = kx\) where \(k\) is the constant of variation. To find the constant of variation, we can equate the two equations.

Step 2 ：Step 2: Equating the equations, we get \(3x + 2 = 5x - 1\)

Step 3 ：Step 3: Simplifying the equation, we get \(2x = 3\)

Step 4 ：Step 4: Solving for \(x\), we get \(x = \frac{3}{2}\)

Step 5 ：Step 5: Substitute \(x = \frac{3}{2}\) into the first equation \(y = 3x + 2\), we get \(y = 3(\frac{3}{2}) + 2 = \frac{9}{2} + 2 = \frac{13}{2}\)

Step 6 ：Step 6: Thus, the direct variation equation is \(y = \frac{13}{2}x\)