$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 4 x -5 y =43\\ -3 x -7 y = 0 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}4\ & -5 \\ -3&-7 \\ \end{array}= 4 \cdot \left(-7\right) -\left(-5\right) \cdot \left(-3\right)=-43 \\ D_x=\begin{array}{|cc|}43\ & -5 \\ 0&-7 \\ \end{array}= 43 \cdot \left(-7\right) -\left(-5\right) \cdot 0=-301 \\ D_y=\begin{array}{|cc|}4\ & 43 \\ -3&0 \\ \end{array}= 4 \cdot 0 -43 \cdot \left(-3\right)=129 \\ \ x=\frac{-301}{-43} \\ x=7 \\ y=\frac{129}{-43} \\ y=-3 \\ L=\{7/-3\}\\ \, \end{array}$