$\definecolor{red}{RGB}{255,0,0}$$\definecolor{black}{RGB}{0,0,0}$
  1. $a_1$
  2. $a_1$
  3. $a_1$
  1. $b_1$
  2. $b_1$
  3. $b_1$
  1. $a_2$
  2. $a_2$
  3. $a_2$
  1. $b_2$
  2. $b_2$
  3. $b_2$
  1. $x_i$
  2. $x_i$
  3. $x_i$
    • $$\color{blue}{\rightarrow}\color{black}\;x_i \;= \;\frac{b_2-b_1}{a_1-a_2}$$
  1. $y_i$
  2. $y_i$
  3. $y_i$
    • $$\color{blue}{\rightarrow}\color{black}\;y_i \;= \;\frac{a_1\cdot b_2-a_2\cdot b_1}{a_1-a_2}$$
Intersection point of two lines

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If the equations are of the form A x + B y + C = 0 calculate first a=-A/B; b=-C/B

Numbers in the form 1/2 or 0.5 or 1.5E3 are accepted: