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# Facts That Matter - Pair of Linear Equations in TwoVariables Class 10 Notes | EduRev

## Class 10 : Facts That Matter - Pair of Linear Equations in TwoVariables Class 10 Notes | EduRev

The document Facts That Matter - Pair of Linear Equations in TwoVariables Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
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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 ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’.
• General Form of a Pair of Linear Equations in Two Variable
General form of a linear pair of equations in two variables is:
a1x + b1y + c= 0  and
a2x + b2y + c2 = 0
where a1, b1, c1, a2, b2, c2 are real numbers such that
a12 + b12 ≠ 0  and  a22 + b22 ≠ 0
• Solution of a Pair of Linear Equations in Two Variables
The solution of a linear equation in two variables ‘x’ and ‘y’ is a pair of values (one for ‘x’ and other for ‘y’) 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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