Ta có : y - x = xy
\(\\\Rightarrow\) y = xy - x
Mặt khác : 4x + 3y = 5xy
\(\Rightarrow\) y = \(\dfrac{5xy-4x}{3}\)
Vì kết quả cùng là y, cho nên :
\(\Rightarrow\)xy - x = \(\dfrac{5xy-4x}{3}\)
\(\Rightarrow\)\(\dfrac{3xy-3x}{3}=\dfrac{5xy-4x}{3}\)
\(\Rightarrow3xy-3x=5xy-4x\\ \Rightarrow3xy-5xy=-4x+3x\\ \Rightarrow-2xy=-x\\ \Rightarrow2xy=x\\ \Rightarrow\dfrac{2xy}{x}=\dfrac{x}{x}\\ \Rightarrow2y=1\Rightarrow y=\dfrac{1}{2}.\)
Tìm x theo y, ta có thể chọn 1 trong 2 phương trình :
\(y-x=xy\)
\(\Rightarrow\dfrac{1}{2}-x=\dfrac{1}{2}x\\ \Rightarrow\dfrac{1}{2}-x-\dfrac{1}{2}x=0\\ \Rightarrow\dfrac{1}{2}-\dfrac{3}{2}x=0\\ \Rightarrow x=\dfrac{1}{2}:\dfrac{3}{2}=\dfrac{2}{6}\)
Vậy, \(y=\dfrac{1}{2};x=\dfrac{2}{6}\)
