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- Pair of Linear Equations in Two Variables : Introduction

If two linear equations have the two same variables, they are called a pair of linear equations in two variables. Following is the most general form of linear equations:

Here, a1, a2, b1, b2, c1 and c2 are real numbers such that;

A pair of linear equations can be represented and solved by the following methods:

- Graphical method
- Algebraic method

For a given pair of linear equations in two variables, the graph is represented by two lines.

- If the lines intersect at a point, that point gives the unique solution for the two equations. If there is a unique solution of the given pair of equations, the equations are called consistent.
- If the lines coincide, there are indefinitely many solutions for the pair of linear equations. In this case, each point on the line is a solution. If there are infinitely many solutions of the given pair of linear equations, the equations are called dependent (consistent).
- If the lines are parallel, there is no solution for the pair of linear equations. If there is no solution of the given pair of linear equations, the equations are called inconsistent.

There are following methods for finding the solutions of the pair of linear equations:

- Substitution method
- Elimination method
- Cross-multiplication method

If a pair of linear equations is given by then following situations can arise.

Situation 1:

In this case, the pair of linear equations is consistent. This means there is unique solution for the given pair of linear equations. The graph of the linear equations would be two intersecting lines.

Situation 2:

In this case, the pair of linear equations is inconsistent. This means there is no solution for the given pair of linear equations. The graph of linear equations will be two parallel lines.

Situation 3:

In this case, the pair of linear equations is dependent and consistent. This means there are infinitely many solutions for the given pair of linear equations. The graph of linear equations will be coincident lines.

- 10th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2015

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Introduction
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NCERT Solution - Exercise 3.1
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NCERT Solution - Exercise 3.2 Part-1
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NCERT Solution - Exercise 3.2 Part-2
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NCERT Solution - Exercise 3.3 Part-1
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NCERT Solution - Exercise 3.3 Part-2
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NCERT Solution - Exercise 3.4 Part-1
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NCERT Solution - Exercise 3.4 Part-2
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NCERT Solution - Exercise 3.5 Part-1
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NCERT Solution - Exercise 3.5 Part-2
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NCERT Solution - Exercise 3.6 Part-1
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NCERT Solution - Exercise 3.6 Part-2
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NCERT Solution - Exercise 4.1 Part-1
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NCERT Solution - Exercise 4.1 Part-2
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NCERT Solution - Exercise 4.2 Part-1
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NCERT Solution - Exercise 4.2 Part-2
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NCERT Solution - Exercise 4.2 Part-3
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NCERT Solution - Exercise 4.3 Part-1
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NCERT Solution - Exercise 4.3 Part-2
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NCERT Solution - Exercise 4.3 Part-3
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NCERT Solution - Exercise 4.3 Part-4
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NCERT Solution - Exercise 4.3 Part-5
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NCERT Solution - Exercise 4.4 Part-1
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NCERT Solution - Exercise 4.4 Part-2
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Solution of Exercise 5.1 (NCERT)-Part-1
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Solution of Exercise 5.1 (NCERT)-Part-2
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Solution of Exercise 5.1 (NCERT)-Part-3.1
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Solution of Exercise 5.1 (NCERT)-Part-3.2
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Solution of Exercise 5.2 (NCERT) Part -1
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Solution of Exercise 5.2 (NCERT) Part -2
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Solution of Exercise 5.2 (NCERT) Part -3
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Solution of Exercise 5.2 (NCERT) Part -4
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Solution of Exercise 5.2 (NCERT) Part -5
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Solution of Exercise 5.2 (NCERT) Part -6
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Solution of Exercise 5.3 (NCERT)Part -1
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Solution of Exercise 5.3 (NCERT)Part - 2
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Solution of Exercise 5.3 (NCERT)Part - 3
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Solution of Exercise 5.3 (NCERT)Part - 4
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Solution of Exercise 5.3 (NCERT)Part - 5
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Solution of Exercise 5.3 (NCERT)Part - 6
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Solution of Exercise 5.3 (NCERT)Part - 7
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Solution of Exercise 5.3 (NCERT)Part - 8
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Solution of NCERT Exercise 5.4 (Optional)
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Introduction : Theorems
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NCERT Solution of Exercise 6.1
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NCERT Solution Exercise 6.2 Part - I
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NCERT Solution Exercise 6.2 Part - II
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NCERT Solution Exercise 6.2 Part - III
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NCERT Solution of Exercise 6.3 Part - III
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NCERT Solution of Exercise 6.4
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NCERT Solution of Exercise 6.5
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NCERT Solution of Exercise 6.5 Part - 2
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NCERT Solution of Exercise 6.6 - Part - 1
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NCERT Solution of Exercise 6.6 - Part - 2
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THEOREM 1:
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Solution of NCERT Exercise 10.1
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Solution of NCERT Exercise 10.2
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Solution of NCERT Exercise 10.2 - Part 2
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Solution of NCERT Exercise 10.2 - part - 3
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Solution of NCERT Exercise 10.2 - part - 4
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Solution of NCERT Exercise 10.2 - part - 5
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Solution of NCERT Exercise 10.2 - part - 6
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