Pair of Linear Equations in Two Variables Class 10 Notes: Revision notes for CBSE Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables have been presented in the article along with a PDF download link. These revision notes on Pair of Linear Equations in Two Variables have been prepared on the basis of the CBSE Class 10 Maths Syllabus 2024. The revision notes are especially for CBSE Class 10 Board Exams 2024 board aspirants.
The revision notes presented here have been prepared after a thorough analysis of the chapter. A few methods of solving exercise questions have also been presented to guide you in solving the NCERT exercises. These handwritten short notes will assist you in preparing for the examinations while saving you a lot of time. They are also great at helping students in doing easy and quick revision.
Revision Notes for CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
The revision notes for Pair of Linear Equations in Two Variables have been attached below for students of the current academic session 2023-2024. Use the PDF download link to save the revision notes for future use.
- A pair of linear equations that has no solution is called an inconsistent pair of linear equations.
- A pair of linear equations in two variables, which has a solution, is called a consistent pair of linear equations.
- A pair of linear equations which are equivalent has infinitely many distinct common solutions. Such a pair is called a dependent pair of linear equations in two variables.
- Parallel lines are inconsistent, when lines intersect at a single point, they are consistent, and when lines may be coincident they are dependent.
- The substitution method is used by substituting a third equation in the already existing equation, to find the values of all the variables. Apart from this, the graphical method is also used. The third method is the elimination method, where one variable is completely removed
- The process used in the substitution method:
Step 1: Find the value of one variable, say y in terms of the other variable, i.e., x from either equation, whichever is convenient.
Step 2: Substitute this value of y in the other equation, and reduce it to an equation in one variable, i.e., in terms of x, which can be solved. Sometimes, as in Examples 9 and 10 below, you can get statements with no variable. If this statement is true, you can conclude that the pair of linear equations has infinitely many solutions. If the statement is false, then the pair of linear equations is inconsistent.
Step 3: Substitute the value of x (or y) obtained in Step 2 in the equation used in Step 1 to obtain the value of the other variable.
- The process used in elimination method:
Step 1: First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal.
Step 2: Then add or subtract one equation from the other so that one variable gets eliminated. If you get an equation in one variable, go to Step 3. If in Step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions. If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.
Step 3: Solve the equation in one variable (x or y) so obtained to get its value.
Step 4: Substitute this value of x (or y) in either of the original equations to get the value of the other variable
For complete Pair of Linear Equations in Two Variables Class 10 Short Notes, click on the link below