\begin{align} \left\{ \begin{array}{l} y = a_1x+b_1 \\ y = a_2x+b_2 \end{array} \right. \end{align} If $a_1 \ne a_2$, \begin{align} \left\{ \begin{array}{l} x = -\dfrac{b_2-b_1}{a_2-a_1} \\ y = \dfrac{a_2b_1-a_1b_2}{a_2-a_1} \end{array} \right. \end{align}

\begin{align} \left\{ \begin{array}{l} y_1 = ax_1+b \\ y_2 = ax_2+b \end{array} \right. \end{align} If $x_1 \ne x_2$, \begin{align} \left\{ \begin{array}{l} a=\dfrac{y_2-y_1}{x_2-x_1}\\ b=\dfrac{x_2y_1-x_1y_2}{x_2-x_1} \end{array} \right. \end{align}