If you want full marks in algebra part, JKBOSE Class 10th Maths Pair of Linear Equations Notes must be clear in your mind. This is Chapter 3 of JKBOSE 10th Maths, and questions from solving equations by substitution or elimination are asked every year.
When I gave my Class 10 board exam, one full question came from elimination method. It was straight from NCERT pattern. If you practice properly, this chapter is very scoring.
Quick Summary – JKBOSE 10th Maths Chapter 3
| Topic | Details |
|---|---|
| Chapter | Pair of Linear Equations in Two Variables |
| Class | 10th JKBOSE |
| Main Methods | Graphical, Substitution, Elimination |
| Common Marks Area | 3–4 mark full question |
| Level | Moderate but scoring |
What is a Pair of Linear Equations
A pair of linear equations in two variables is a set of two equations that contain two variables.
General form:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Here x and y are variables.
Graphical Method Class 10 JKBOSE
In graphical method, you draw both equations on graph paper. The point where the two lines intersect is the solution.
- If lines intersect at one point → One solution
- If lines are parallel → No solution
- If lines overlap → Infinite solutions
Graph questions usually carry 3 or 4 marks. Draw neat graph and label axes properly.
Algebraic Methods to Solve Equations
1. Substitution Method
Step 1 – Express one variable in terms of the other.
Step 2 – Substitute into second equation.
Step 3 – Solve and find value of one variable.
Step 4 – Substitute back to get other variable.
Example:
x + y = 5
x − y = 1
From first equation: x = 5 − y
Substitute in second:
5 − y − y = 1
5 − 2y = 1 → 2y = 4 → y = 2
x = 3
2. Elimination Method
Step 1 – Make coefficients of one variable same.
Step 2 – Add or subtract equations to eliminate one variable.
Step 3 – Find remaining variable.
Example:
2x + 3y = 13
4x + 3y = 19
Subtract first from second:
2x = 6 → x = 3
Substitute to find y.
This method is faster in exam. I personally preferred elimination method.
Conditions for Number of Solutions
For equations:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
| Condition | Result |
|---|---|
| a₁/a₂ ≠ b₁/b₂ | One Solution |
| a₁/a₂ = b₁/b₂ ≠ c₁/c₂ | No Solution |
| a₁/a₂ = b₁/b₂ = c₁/c₂ | Infinite Solutions |
Condition-based question is common in JKBOSE 10th Maths Chapter 3.
Word Problems from Pair of Linear Equations Class 10 JKBOSE
Most students lose marks in word problems because they write wrong equations.
Steps to solve:
- Assume variables clearly
- Convert statement into equations
- Solve using elimination or substitution
- Write final answer with units
Practice at least 5 word problems before exam.
Important Questions for Practice
1. Solve by substitution method: 2x + y = 11, x − y = 1
2. Solve by elimination method: 3x + 2y = 11, 2x − y = 4
3. Find number of solutions of 2x + 3y = 5 and 4x + 6y = 10
4. Solve graphically: x + y = 4, x − y = 2
5. Solve word problem on age or mixture
Exam Tips from Dar Zaid
Best method: Use elimination if coefficients are simple.
Graph question: Draw table of at least two points for each line.
Common mistake: Students forget to check final answer in both equations. Always verify.
Time tip: Attempt this after finishing short algebra chapters like Real Numbers and Polynomials.
Frequently Asked Questions
How many marks does Pair of Linear Equations carry in JKBOSE?
Usually one full 3 or 4 mark question appears from this chapter in JKBOSE Class 10 Maths paper.
Which method is best for solving linear equations?
The elimination method is usually faster in the exam if the coefficients are simple and easy to cancel.
What is graphical method in Class 10 JKBOSE?
In the graphical method, both equations are drawn on graph paper. The point where the two lines intersect gives the solution of the equations.
Can Pair of Linear Equations have no solution?
Yes. If a₁/a₂ = b₁/b₂ but not equal to c₁/c₂, then the lines are parallel and there is no solution.
Is Chapter 3 important for JKBOSE board exam?
Yes. It is one of the main algebra chapters and carries good marks every year in the JKBOSE Class 10 Maths exam.
Next, revise JKBOSE Class 10th Maths Polynomials Notes and practice previous year papers to stay confident.
