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An algebraic expression having higher exponent of variable one , is known as linear equation or linear expression.

for example : 4x + 2 = 0,   2x + 4y = 10 and etc.

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Linear Equation of one variable :

The expressions with only one variable are called Linear Equations in one variable.

for example : 6x - 12 = 6,

How to solve linear equation in one variable :

there are many method to solve linear equation in one variable such as

(i) . Cross multiplication

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(ii) . Grouping the same variable in same side.

(iii) . Reducing the expression in proper form.

2x - 8 = 0

2x = 8

x = 4.

Linear equation of two variable

linear equations in two variables are the equations in which two variables are present, so in this case there are two unknown variables. This type of equation has many real life applications.

for example: 3x + 9y = 12, in this case x and y are two variables.

Method to solve linear equation of two variables

Let the given linear equation in two variables be ax+ by +c, where a ≠ zero and b ≠ zero. Then, for finding its solution, we use the following steps

(i) . Put an arbitrary value of x (or y) in the given equation and find the corresponding value of the second variable. Thus we get one pair of the solution of the given equation.

(ii) . Repeat step 1 for another arbitrary value of x (or y) and get another pair of a solution of given equation.

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Solution of pair of linear equation :

(a) . Geometric method : In this method we plot both the lines and the point at which both line intersect will be the answer

(b) . Algebraic method :

(i). Method of subsitution

(ii) . Method of Elimination

(iii) . Cross multiplication method

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Inconsistent pair of linear equations: A pair of linear equations which has no solution.

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Consistent pair of linear equations: A pair of linear equations which has a solution.(either one solution or infinite solution)

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Independent pair of linear equations – If the pair of equations has only one solution.

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Dependent pair of linear equations – If the pair of equations has infinite solutions.

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Comparision	Graphical representation	Solution
(a1/a2) ≠ (b1/b2)	intersecting line	one solution
(a1/a2) = (b1/b2) = (c1/c2)	coincident or identical lines	many solutions or infinite solution
(a1/a2) = (b1/b2) ≠ (c1/c2)	parallel lines	no solution