$$\begin{gathered} \frac{x+1}{3}+\frac{y-1}{4}=4 /·\left(3·4\right) \wedge \\ \frac{x-2}{3}-\frac{y+3}{2}=-2 /·\left(2·3\right) \end{gathered}$$

$$\begin{gathered} \frac{x+1}{3}+\frac{y-1}{4}=4 /·12 \wedge \\ \frac{x-2}{3}-\frac{y+3}{2}=-2 /·6 \end{gathered}$$

$$\begin{gathered} \frac{12·\left(x+1\right)}{3}+\frac{12·\left(y-1\right)}{4}=4·12 \wedge \\ \frac{6·\left(x-2\right)}{3}-\frac{6·\left(y+3\right)}{2}=-2 ·6 \end{gathered}$$

$$\begin{gathered} 4·\left(x+1\right)+3·\left(y-1\right)=4·12 \wedge \\ 2·\left( x-2\right)-3·\left(y+3\right)=\left(-2\right)·6 \end{gathered}$$

$$\begin{gathered} 4·x+4·1+3·y-3·1=4·12 \wedge \\ 2· x+\left(-2\right)·2+(-3)·y+(-3)·3=\left(-2\right)·6 \end{gathered}$$

$$\begin{gathered} 4·x+4+3·y-3=48 \wedge \\ 2· x+\left(-4\right)+(-3·y)+(-9)=-12 \end{gathered}$$

$$\begin{gathered} 4·x+3·y+1=48 \wedge \\ 2· x+(-13)+(-3·y)=-12 \end{gathered}$$

$$\begin{gathered} 4·x+3·y+1=48 \wedge \\ 2· x-13-3·y=-12 \end{gathered}$$

$$\begin{gathered} 4·x+3·y=48-1 \wedge \\ 2· x-3·y=-12+13 \end{gathered}$$

$$\begin{gathered} 4·x+3·y=47\wedge \\ 2· x-3·y=1 \end{gathered}$$

$$\begin{gathered} 4·x+3·y=47\wedge \\ 2· x\mathbf{-}\mathbf{3}\mathbf{·}\mathit{y}=1 \end{gathered}$$

$$6x=48, x=\frac{48}{6}, x=8$$

$$2·8-3·y=1, 16-3·y=1, -3·y=1-16, -3·y=-15, y=\frac{-15}{-3}, y=5$$