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RD Sharma Solutions

RD Sharma Class 12 Maths Solutions Chapter 8 - Solution of Simultaneous Linear Equations

RD Sharma Class 12 Maths Solutions Chapter 8 - Solution of Simultaneous Linear Equations

Introduction to Solution of Simultaneous Linear Equations - Free PDF Download

Students can download RD Sharma Class 12 Solution of Simultaneous Linear Equations from Vedantu for free of cost. By practicing these solutions they will be able to get their doubts cleared instantly. RD Sharma Class 12 Chapter 8 Maths will help them to score well in Mathematics board exams as well as in competitive exams. We mainly focus on providing answers, which are in an easy-to-understand format, and further help students to clearly understand and remember the important formulae.

Introduction to RD Sharma Class 12 Chapter 8 Maths

The simultaneous equation model is a statistical model in which the dependent variable is a function of other dependent variables, not just like the independent variable. To solve the linear equation we have to look for the variable values that make all equations true at the same time. In this Pdf, our experts are providing detailed solutions of simultaneous linear equations that will help students to understand the concept easily. RD Sharma Class 12 Chapter 8 Maths mainly focuses on the homogeneous and non-homogeneous system of equations. Following are some of the important concepts that are discussed in this chapter.

Definition and Meaning of Consistent System

Homogeneous and non-homogeneous systems

The matrix method for the solution of a non-homogeneous system

To solve the given system of linear equations when the coefficient matrix is nonsingular.

To solve the given system of equations when the coefficient matrix is singular

To solve a system of linear equations when the inverse of the coefficient matrix is obtained

Applications of simultaneous linear equations

The solution of the homogeneous system of linear equations requires

The determinant of the coefficient matrix is a non-singular matrix
The determinant of the coefficient matrix is a singular matrix.

The Process of Framing Simultaneous Linear Equations from Mathematical Problems are:

To solve simultaneous system equations by the method of comparison and method of elimination
To acquire the ability to solve a simultaneous system of equations by the method of substitution and method of cross-multiplication.
We should know the condition for a pair of linear equations to become simultaneous equations
To acquire the ability to solve mathematical problems by framing simultaneous equations.

Exercises in RD Sharma Class 12 Chapter 8 Maths

Exercise 8.1
Exercise 8.2

Preparation Tips to Solve Simultaneous Linear Equations

In the pdf, we have provided quick and easy tips and tricks for students on Linear Equation questions which and efficiently in competitive exams as well as other recruitment exams.

Simultaneous linear equations can be easily solved by eliminating the wrong options. It means to put the given values in the equation and check which one is satisfying the equation.

Always start to solve from standard form of linear equations is y= mx+b

Reasons to Use Our Solutions for Chapter 12 Maths

Studying from the RD Sharma Solutions for Class 12 Maths - Solution of Simultaneous Linear Equations created by these experts is one of the most useful strategies a CBSE Class 12 student can follow in order to score high and get a better rank. Several studies on former class 12 students have shown that using this study material as a supplementary strategy to prepare for CBSE Class 12 board examination is actually beneficial. Even if a student reads and tries to memorize the Class 12 textbook cover to cover, it would not be as beneficial as studying both of the things together.

Instead, students can use the RD Sharma Solutions for Class 12 Maths - Solution of Simultaneous Linear Equations by tapping on a link provided on this page. This link will take the students to a download page where they will be asked for their Gmail ID. After signing in, they will get access to the PDF version of RD Sharma Solutions for Class 12 Maths - Solution of Simultaneous Linear Equations.

This study material is completely free of charge. That's because we, at Vedantu, believe that in order to reach out to as many students as we can, we have to sacrifice something. And that's why we decided to give away our valuable and expertly-created study materials for free.

We also have created a mobile app for students who like to use apps for convenience. Yes, that app will provide a better user experience and convenience to the users. Students can download the app from Google Play Store. This app is available across all devices which includes mobile phones and tablets.

Conclusion

For students who wish to get excellence in their exams and build their confidence level high, the best is to practise RD Sharma Class 12 Solution of Simultaneous Linear Equations available at Vedantu website in PDF format. On the regular practice of these questions, students can speed up the method of solving problems by using short-cut tips to secure high marks in their examination. Sometimes, it leads to a unique solution, but for some systems, it shows there are no solutions, and for other systems, it produces infinitely many solutions.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 8 - Solution of Simultaneous Linear Equations

1. How do Vedantu's RD Sharma Solutions help with Chapter 8, 'Solution of Simultaneous Linear Equations'?

These solutions provide detailed, step-by-step answers for every problem in the RD Sharma textbook. They focus on the matrix method (using the inverse of a matrix) as prescribed by the CBSE syllabus, helping you master the correct approach for your exams. They are perfect for practising a wide variety of questions beyond the NCERT textbook.

2. Is the chapter on solving linear equations in RD Sharma difficult for Class 12 students?

This chapter is generally considered scoring and logical. The main challenge lies in correctly calculating the determinant and inverse of a matrix without making calculation errors. Practising the diverse problems from RD Sharma helps build both speed and accuracy, making the chapter easier to master.

3. What is the main method for solving simultaneous linear equations in the Class 12 syllabus?

The primary method prescribed by the CBSE for Class 12 is the matrix method. This involves representing the system of equations in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The solution is then found using the formula X = A⁻¹B, provided that the inverse of matrix A exists.

4. Why should I use RD Sharma solutions for this topic if I am already using the NCERT book?

While NCERT provides the foundational concepts, RD Sharma offers a much larger and more varied set of problems. Using these solutions helps you:

Practise more complex and challenging questions.
Gain confidence in handling different types of equation systems.
Reinforce your understanding of concepts like consistency and inconsistency of systems.

5. How can I check if a system of linear equations is consistent or inconsistent?

To check for consistency using the matrix method, first calculate the determinant of the coefficient matrix A (det(A) or |A|). If det(A) ≠ 0, the system is consistent and has a unique solution. If det(A) = 0, you must then calculate (adj A)B. If (adj A)B = O (the zero matrix), the system is consistent with infinitely many solutions. If (adj A)B ≠ O, the system is inconsistent and has no solution.

6. What is a common mistake to avoid when solving linear equations using the matrix inverse method?

A very common error is making a mistake while calculating the adjoint of the matrix (adj A) or its determinant (det(A)). A small sign error in the cofactor matrix or a calculation slip in the determinant will lead to a completely incorrect inverse, and therefore, a wrong final answer. It is crucial to double-check these calculations carefully.

7. Do these solutions cover problems for both two-variable and three-variable systems?

Yes, the RD Sharma solutions for Class 12 Chapter 8 comprehensively cover the methods for solving systems of linear equations for both two and three variables. The step-by-step approach is clearly demonstrated for each type, ensuring you understand how the process scales from simpler to more complex systems.