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**Facts that Matter**

**Linear Equation in Two Variable**

An equation which can be put in the form

ax + by + c = 0

where a, b and c are real numbers (a, b â‰ 0) is called a linear equation in two variables â€˜xâ€™ and â€˜yâ€™.**General Form of a Pair of Linear Equations in Two Variable**

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

a_{1}x + b_{1}y + c_{1 }= 0 and

a_{2}x + b_{2}y + c_{2}= 0

where a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2}are real numbers such that

a_{1}^{2}+ b_{1}^{2}â‰ 0 and a_{2}^{2}+ b_{2}^{2}â‰ 0**Solution of a Pair of Linear Equations in Two Variables**

The solution of a linear equation in two variables â€˜xâ€™ and â€˜yâ€™ is a pair of values (one for â€˜xâ€™ and other for â€˜yâ€™) 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

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.

(iii) 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.

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178 videos|268 docs|103 tests

### Elimination Method Part 2

- Video | 12:01 min
### Test: Elimination Method

- Test | 10 ques | 10 min
### Test: Cross Multiplication Method

- Test | 10 ques | 10 min
### Equation Reducible to Linear Form

- Video | 15:07 min
### Test: Equations Reducible To Linear Form

- Test | 20 ques | 20 min

- Test: Pair Of Linear Equations In Two Variables - 3
- Test | 25 ques | 25 min
- Test: Substitution Method
- Test | 10 ques | 10 min