Algebra
# System of Linear Equations

Let $\text{Max}(x, y)$ and $\text{Min}(x, y)$ be defined as follows for real numbers $x$ and $y:$ $\text{Max}(x, y)=\begin{cases} x \quad (x\ge y) \\ y \quad (x<y), \\ \end{cases}\\ \text{Min}(x, y)=\begin{cases} x \quad (x< y) \\ y \quad (x\ge y). \end{cases}$

If the following holds for distinct numbers $x$ and $y,$ what is $3xy:$ $\text{Max}(x, y)=5x-2y+79, \quad \text{Min}(x, y)=4x+3y-47?$