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 \(3xy:\) \[\text{Max}(x, y)=5x-2y+79, \quad \text{Min}(x, y)=4x+3y-47?\]

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