\(\dfrac{x-7}{7}=\dfrac{y-6}{6}=\dfrac{x-y-1}{1}=\dfrac{-4-1}{1}=-5\)
\(\Rightarrow x-7=7.\left(-5\right)=-35\Rightarrow x=-28;y-6=6.\left(-5\right)=-30\Rightarrow y=-24\)
\(\Leftrightarrow6\left(x-7\right)=7\left(y-6\right)\)
\(\Leftrightarrow6x-42=7y-42\)
\(\Leftrightarrow6x=7y\)
\(\Leftrightarrow6\left(x-y\right)-y=0\)
\(\Leftrightarrow-24-y=0\)
\(\Leftrightarrow y=-24\)
\(\Leftrightarrow\dfrac{x-7}{-24-6}=\dfrac{7}{6}\Leftrightarrow\dfrac{x-7}{-30}=\dfrac{7}{6}\Leftrightarrow6x-30=-210\Leftrightarrow6x=-180\Leftrightarrow x=-30\)
\(\dfrac{x-7}{y-6}=\dfrac{7}{6}\Rightarrow6\left(x-7\right)=7\left(y-6\right)\Rightarrow6x-42=7y-42\Rightarrow6x=7y\Rightarrow\)\(\dfrac{x}{7}=\dfrac{y}{6}\)
Áp dụng tính chất DTSBN, ta có:
\(\dfrac{x}{7}=\dfrac{y}{6}=\dfrac{x-y}{7-6}=\dfrac{4}{1}=4\)
\(\Rightarrow\)\(\dfrac{x}{7}=4\Rightarrow x=28\)
\(\Rightarrow\)\(\dfrac{y}{6}=4\Rightarrow y=24\)
