BSE Odisha Class 10 Maths Chapter 1: Sarala Sahasamikaran (ସରଳ ସହସମୀକରଣ) One Shot

Sarala Sahasamikaran, also called Linear Simultaneous Equations, is Chapter 1 of the Algebra book in BSE Odisha Class 10 Maths. It is a scoring chapter if you know when to use which method. This one-shot session by Abhisek Sir on the PW Odisha 9th & 10th channel covers the whole chapter in Odia. It runs a little over two hours, from concepts to word problems to expected MCQs.

Below you'll find the video, a timestamp guide, the key formulas, and solved examples to practise alongside it.

Watch BSE Odisha Chapter 1 Linear Simultaneous Equations in ONE SHOT 

Students can watch the Sarala Sahasamikaran One Shot to cover and revise the complete Linear Simultaneous Equations chapter in one session, including key concepts, solving methods, applications, board questions, and final revision.

BSE Odisha Class 10 Maths Chapter 1: Sarala Sahasamikaran  Video Timestamps

BSE Odisha Class 10 Chapter 1 Maths video timestamps: 

Key Formulas at a Glance

Write the two equations in standard form:

a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0

Conditions for Consistency

Cross-Multiplication Formula

x / (b₁c₂ − b₂c₁) = y / (c₁a₂ − c₂a₁) = 1 / (a₁b₂ − a₂b₁)

Cramer's Rule (Determinant Method)

For a₁x + b₁y = c₁ and a₂x + b₂y = c₂:

• D = a₁b₂ − a₂b₁

• Dₓ = c₁b₂ − c₂b₁

• Dᵧ = a₁c₂ − a₂c₁

• x = Dₓ / D and y = Dᵧ / D, provided D ≠ 0

Solved Examples

Example 1: Substitution Method

Solve x + y = 7 and 2x − y = 2.

From the first equation, y = 7 − x.
Substitute into the second: 2x − (7 − x) = 2, so 3x = 9 and x = 3.
Then y = 7 − 3 = 4.

Answer: x = 3, y = 4. Check: 2(3) − 4 = 2 ✓

Example 2: Elimination Method

Solve the system of equations 3x + 2y = 12 and 5x − 2y = 4.

The y-coefficients are equal and opposite, so add the equations: 8x = 16, so x = 2.
Put x = 2 in the first equation: 6 + 2y = 12, so y = 3.

Answer: x = 2, y = 3. Check: 5(2) − 2(3) = 4 ✓

Example 3: Cross-Multiplication Method

Solve 2x + 3y − 13 = 0 and 3x − y − 3 = 0.

Here a₁ = 2, b₁ = 3, c₁ = −13 and a₂ = 3, b₂ = −1, c₂ = −3.

• a₁b₂ − a₂b₁ = −2 − 9 = −11

• b₁c₂ − b₂c₁ = −9 − 13 = −22, so x = −22 / −11 = 2

• c₁a₂ − c₂a₁ = −39 + 6 = −33, so y = −33 / −11 = 3

Answer: x = 2, y = 3. Check: 2(2) + 3(3) = 13 ✓

Example 4: Word Problem

5 pens and 3 notebooks cost ₹95. 2 pens and 4 notebooks cost ₹80. Find the price of one pen and one notebook.

Let a pen cost ₹x and a notebook cost ₹y.
The equations are 5x + 3y = 95 and 2x + 4y = 80, which simplifies to x + 2y = 40.
So x = 40 − 2y. Substituting: 5(40 − 2y) + 3y = 95, so 200 − 7y = 95 and y = 15.
Then x = 40 − 30 = 10.

Answer: a pen costs ₹10 and a notebook costs ₹15.

Which Method Should You Use in the Exam?

• Substitution: best when one variable already has a coefficient 1.

• Elimination: best when coefficients can be matched quickly.

• Cross-multiplication: best when the equations are in standard form and the numbers are awkward.

• Cramer's Rule: a fast, mechanical check once you know the determinant pattern.

For word problems, define your variables first, form two equations, and verify the answer against the original statement.

Sarala Sahasamikaran One Shot: Complete Chapter Coverage

The video covers the following topics from Linear Simultaneous Equations, making it useful for students who want to revise the chapter from basics to board-exam questions:

1. Introduction to Linear Simultaneous Equations – Basic concept and meaning of simultaneous equations.

2. Standard Form of Simultaneous Equations – Understanding and writing equations in standard form.

3. Conditions for Consistency and Types of Solutions – Different possible solution cases.

4. Graphical Representation of Simultaneous Equations – Understanding solutions through graphs.

5. Substitution Method – Solving simultaneous equations using substitution.

6. Elimination Method – Finding solutions by eliminating one variable.

7. Cross-Multiplication Method – Solving equations using the cross-multiplication formula.

8. Cramer’s Rule / Determinant Method – Using determinants to solve the equations.

9. Solving Word Problems Using Simultaneous Equations – Converting given situations into equations.

10. Application-Based Questions – Practice using simultaneous equations.

11. Important Board Exam Questions – Questions relevant to exam preparation.

12. Expected MCQs – Objective-type questions for quick practice.

13. Common Mistakes and Short Tricks – Important points to avoid errors while solving.

14. Quick Revision of Important Formulas – Formula-based chapter revision.

15. Final Board Exam Revision – Quick recap of the complete chapter.

How to Use This One Shot for Revision

1. Watch the video once, pausing at each timestamp to try the question yourself first.

2. Write the consistency table and formulas on a one-page sheet.

3. Practise one question per method from your Algebra textbook.

4. Finish with the expected MCQs section (from 2:01:45) as a final self-test.

5. Revisit word problems the day before the exam, since they need practice more than memorisation.