 # linear equation in 2 variables

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## 03 LINEAR EQUATION IN 2 VARIABLES:

Linear equation in two variables: It is the equation with two variables and with highest

power of  variable or Degree .

General form:

Solution of Linear equation in two variables: The values of  and  which satisfy the given

equation is called solution of the equation in two variables.

e.g.  2x +3y+4=0 has solution x=1 and y =-2.

X= -5 , Y= 2 is also solution of the equation.

• The linear equation can have infinite solutions.
• The graph of linear equation is a straight line.
• The solution of a linear equation in variables is a point on the line graph.
• Any point on line is the solution of linear equation representing line.

Pair of linear equations in 2 variables:

It contains two linear equations in same two variables

Geometric meaning of Pair of linear equations in  variables:

Case 1:

When two lines intersect at a single point.

• There is unique solution.
• Equations are called consistent.

Case 2:

When two lines coincide with each other

• There are infinitely many solution
• Equations are called consistent

Case 3:

When two lines are parallel.

• No solution exist
• Equations are called inconsistent

Algebraic method to solve pair of linear equations in  variables:

Substitution method:

• Find value of in terms of using any equation:
• Substitute this
${2}^{nd}$

equation i.e. in

• Find the value of  x(or y)
• Put value x(or y) in eq in step 1.

Elimination Method:

• Make coefficients of  x (or y) equal by multiplying with suitable non zero real number.
• Add or subtract both equations.
• Get the value of y( or x).
• Substitute value of y ( or x) in suitable equation and get value of other variable.

Cross multiplication method:

Arrange the coefficients as shown:

And we can write

Equations reducible to a pair linear equation in two variables:

This is pair of linear equations in variables  and .