Question 2: How many pairs (x,y) satisfy \(\frac{x}{4} = \frac{y}{7}\) and xy = 112

\(\begin{array}{l} \frac{x}{4} = \frac{y}{7} = k \Rightarrow \left\{ \begin{array}{l} x = 4k\\ y = 7k \end{array} \right.\\ xy = 112 \Rightarrow 4k.7k = 112 \Rightarrow 28{k^2} = 112\\ \Rightarrow {k^2} = 4 \Rightarrow k = \pm 2\ \ *k = 2 \Rightarrow x = 8,y = 14\\ *k = – 2 \Rightarrow x = – 8;y = – 14 \end{array}\)

So there are two pairs (x,y) satisfying the problem