NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesDefine a pair of linear equations in two variables and state its standard general form.

A pair of linear equations in two variables consists of two algebraic equations of degree one involving the same two variables, usually represented as $x$ and $y$. \nThe standard general form of a pair of linear equations in two variables is given by:

1. $a_1 x + b_1 y + c_1 = 0$
2. $a_2 x + b_2 y + c_2 = 0$ \nHere, $a_1, b_1, c_1, a_2, b_2,$ and $c_2$ are real numbers such that $a_1^2 + b_1^2 \neq 0$ and $a_2^2 + b_2^2 \neq 0$. Geometrically, each equation represents a straight line on a two-dimensional Cartesian plane, and solving the system means finding common point(s) of intersection.