4. Pair of Linear equations in Two Variables

A pair of linear equations in two variables represents two algebraic equations that contain the same two variables, usually written in the form ax + by + c = 0. The solutions of these equations represent values of the variables that satisfy both equations simultaneously. Graphically, each equation represents a straight line, and the solution of the pair is the point where the two lines intersect.

 

In this chapter, students learn different methods to solve such equations, including the graphical method, substitution method, and elimination method. The lesson also explains the different possible situations of two lines: intersecting lines (one solution), parallel lines (no solution), and coincident lines (infinitely many solutions). Understanding these methods helps students solve many real-life problems involving relationships between two quantities.