\(\frac{x+3}{y-1}=\frac{3}{4}\Leftrightarrow4\left(x+3\right)=3\left(y-1\right)\Leftrightarrow4x+12=3y-3\Leftrightarrow4x+15=3y\Leftrightarrow\frac{4}{3}x+5=y;x+y=5\Rightarrow\frac{4}{3}x+5+x=5\Leftrightarrow\frac{7}{3}x=0\Leftrightarrow x=0\Rightarrow y=5.\text{ Vậy: x=0;y=5}\)