CBSE Class 10 Maths Notes Chapter 3 Pair of Linear equations in Two Variables Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 3 Pair of Linear equations in Two Variables. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
CBSE Class 10 Maths Notes Chapter 3 Pair of Linear equations in Two Variables
- For any linear equation, each solution (x, y) corresponds to a point on the line. General form is given by ax + by + c = 0.
- The graph of a linear equation is a straight line.
-
Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is: a
1
x + b
1
y + c
1
= 0; a
2
x + b
2
y + c
2
= 0
where a 1 , a 2 , b 1 , b 2 , c 1 and c 2 are real numbers, such that a 1 2 + b 1 2 ≠ 0, a 2 2 + b 2 2 ≠ 0. - A pair of values of variables ‘x‘ and ‘y’ which satisfy both the equations in the given system of equations is said to be a solution of the simultaneous pair of linear equations.
-
A pair of linear equations in two variables can be represented and solved, by
(i) Graphical method
(ii) Algebraic method
(i) Graphical method.
The graph of a pair of linear equations in two variables is presented by two lines.
(ii) Algebraic methods.
Following are the methods for finding the solutions(s) of a pair of linear equations:
- Substitution method
- Elimination method
- Cross-multiplication method.
- There are several situations which can be mathematically represented by two equations that are not linear to start with. But we allow them so that they are reduced to a pair of linear equations.
- Consistent system. A system of linear equations is said to be consistent if it has at least one solution.
- Inconsistent system. A system of linear equations is said to be inconsistent if it has no solution.
CONDITIONS
FOR CONSISTENCY
Let the two equations be:
a
1
x + b
1
y + c
1
= 0
a
2
x + b
2
y + c
2
= 0
Then,
| Relationship between coeff. or the pair of equations | Graph | Number of Solutions | Consistency of System |
| \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \) | Intersecting lines | Unique solution | Consistent |
| \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { c_{ 1 } }{ c_{ 2 } } \) | Parallel lines | No solution | Inconsistent |
| \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } =\frac { c_{ 1 } }{ c_{ 2 } } \) | Co-incident lines | Infinite solutions | Consistent |
Class 10 Maths Notes
- Chapter 1 Real Numbers Class 10 Notes
- Chapter 2 Polynomials Class 10 Notes
- Chapter 3 Pair of Linear equations in Two Variables Class 10 Notes
- Chapter 4 Quadratic Equations Class 10 Notes
- Chapter 5 Arithmetic Progressions Class 10 Notes
- Chapter 6 Triangles Class 10 Notes
- Chapter 7 Coordinate Geometry Class 10 Notes
- Chapter 8 Introduction to Trigonometry Class 10 Notes
- Chapter 9 Some Applications of Trigonometry Class 10 Notes
- Chapter 10 Circles Class 10 Notes
- Chapter 11 Constructions Class 10 Notes
- Chapter 12 Areas related to Circles Class 10 Notes
- Chapter 13 Surface Areas and Volumes Class 10 Notes
- Chapter 14 Statistics Class 10 Notes
- Chapter 15 Probability Class 10 Notes