Linear equation in two variable
Solution of a linear equation
x = α,γ = β is a solution of the linear equation ax + by + c = 0, if aα + bβ + c = 0. Each solution (α, β) of a linear equation in two variables ax + by + c = 0 corresponds to a point on the line representing the equation in a Cartesian plane and vice versa.
Pair of linear equations in two variables or system of simultaneous linear equation in two variables
Solution of system of simultaneous equation in two variables :
A pair of values of x and y satisfying each in a given system is called solution of given system .
Methods of solving a pair of linear equations in two variables:
There are two methods for solving a pair of linear equations in two variables.
1. Graphical Method 2. Algebraic Method
Plot the graph of two equations in x and y in cartesian plane onthe same graph.
(a) If two lines intersect, then the solution is unique andequations are consistent.
(b) If two lines are parallel, then there is no solution andequations are inconsistent.
(c) If two lines are coincident, then there are infinitely many solutions and equations are consistent.
2. Algebraic Method:
There are three methods for finding solution of a pair of linear equations (i) Substitution method
(ii) Elimination method (iii) Cross-multiplication method.
Cross – multiplication method : If the given system is
This helps us in memorising the solution which is given as under :