# Linear Equations in Two variables CBSE Class 9 Maths Solutions PDF

Linear Equatioins in Two variables Class 9: Basic Concepts with Examples are given below and the solution pdf can be downloaded from the link given in this post.

•    Linear Equation in Two Variables

An equation which can be put in the form

ax + by + c = 0

where a, b and c are real numbers {a, b ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’

•    General Form of a Pair of Linear Equations in Two Variables

General form of a linear pair of equations in two variables is:

a1x + b1y + cx – 0 and

a2x + b2y + c2 = 0

where a1 b1, c1, a2, b2, c2 are real numbers such that

a12 + b12 0 and a22 + b22 0

•    Solution of a Pair of Linear Equations in Two Variables

The solution of a linear equation in two variables ‘x’ and ‘y’ is a pair of values (one for ‘x’ and other for ‘y’)

which makes the two sides of the equation equal.

There are two methods to solve a pair of linear equations:

(i) algebraic method

(ii) graphical method.

•    Algebraic Method

We have already studied (i) Substitution method and (ii) Elimination method. Here, we will study cross-multiplication method also.

If a1 x + b1 y + c1 = 0

a2 x + b2 y + c2 = 0

form a pair of linear equations, then the following three situations can arise:

(i) If then the system is consistent.

(ii) If then the system is inconsistent.

(ii) If then the system is dependent and consistent.

•    Graphical Method of Solution of a Pair of Linear Equations

(i) If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution, i.e., the system is consistent.

(ii) If the graphs of two equations of a system are two parallel lines, the system is said to have no solution, i.e., the system is inconsistent.

(iii) When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions, i.e., the system is consistent and dependent.