Pair of Linear Equations in Two Variables | Class 10 Mathematics Notes

3.2 Graphical Method of Solution of a Pair of Linear Equations

This section explains the graphical method to solve a pair of linear equations in two variables. Each linear equation represents a straight line on the Cartesian plane. The solution to the pair corresponds to the point(s) where these lines intersect. The section defines three types of pairs based on their solutions: consistent pairs (with at least one solution) and inconsistent pairs (with no solution). Further, consistent pairs are divided into independent (unique solution) and dependent (infinitely many solutions). The graphical behavior of the lines is summarized as follows: (i) intersecting lines correspond to a unique solution, (ii) parallel lines correspond to no solution, and (iii) coincident lines correspond to infinitely many solutions. Three example pairs illustrate these cases, with their coefficients compared via ratios a1/a2, b1/b2, and c1/c2 to determine the nature of the solution. The section also includes detailed examples solving pairs graphically by plotting points and drawing lines to find the intersection point representing the solution.

📊 Diagram: See table_1: Table comparing ratios and graphical interpretations; figure_2: Graph showing solution of x + 3y = 6 and 2x - 3y = 12; table_2: Values of x and y used for plotting; figure_3: Graph showing solution of y = 2x - 2 and y = 4x - 4; table_3: Values of x and y for plotting.

🧪 Activity: Plotting points for given equations and drawing lines to find intersection points.

🔗 Connection: Prepares for algebraic methods by understanding graphical nature of solutions.

Table on page 3 (2×8)

| 1. | $x - 2y = 0$

Table on page 4 (5×3)

Table on page 5 (5×3)