Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Exercise 3.2 NCERT Solutions

Introduction

Exercise 3.2 focuses on the graphical method of solving linear equations in two variables. You’ll learn how to plot equations on a graph, find their point of intersection, and interpret solutions. This exercise builds the foundation for understanding consistent, inconsistent, and dependent systems of equations.

Formula Used

• General Form of Linear Equation in Two Variables:

$$$$ax+by+c=0

• Graphical Solution:

  • Plot both equations on the same graph.

  • The point of intersection gives the solution $(x,y)$.

NCERT Questions with Solutions (10)

Q1. Draw the graph of $x+y=5$ and $x-y=1$. Find the solution.

Solution: Equations intersect at $(3,2)$.

Q2. Draw the graph of $2x+y=6$ and $x-y=2$. Find the solution.

Solution: Equations intersect at $(2,2)$.

Q3. Draw the graph of $x+2y=8$ and $2x-y=2$. Find the solution.

Solution: Equations intersect at $(2,3)$.

Q4. Draw the graph of $3x+2y=12$ and $x-y=1$. Find the solution.

Solution: Equations intersect at $(2,1.5)$.

Q5. Draw the graph of $x+y=7$ and $x-y=3$. Find the solution.

Solution: Equations intersect at $(5,2)$.

Q6. Draw the graph of $2x+3y=12$ and $x-y=4$. Find the solution.

Solution: Equations intersect at $(6,-2)$.

Q7. Draw the graph of $x+y=4$ and $2x-y=2$. Find the solution.

Solution: Equations intersect at $(2,2)$.

Q8. Draw the graph of $3x-y=3$ and $x+y=5$. Find the solution.

Solution: Equations intersect at $(2,3)$.

Q9. Draw the graph of $x-2y=4$ and $2x+y=7$. Find the solution.

Solution: Equations intersect at $(3,-0.5)$.

Q10. Draw the graph of $x+y=10$ and $x-y=2$. Find the solution.

Solution: Equations intersect at $(6,4)$.

FAQs (10 from NCERT)

1. Q: What is the graphical method of solving linear equations? A: Plot both equations on a graph; intersection point gives the solution.

2. Q: What is a consistent system of equations? A: A system that has at least one solution.

3. Q: What is an inconsistent system of equations? A: A system that has no solution (parallel lines).

4. Q: What is a dependent system of equations? A: A system that has infinitely many solutions (same line).

5. Q: How do you plot a linear equation? A: Find two points satisfying the equation and join them.

6. Q: What is the solution of a pair of linear equations? A: The point where both lines intersect.

7. Q: What is the slope of a line? A: Ratio of change in $y$ to change in $x$.

8. Q: What is the intercept form of a line? A: $\frac{x}{a}+\frac{y}{b}=1$.

9. Q: What is the slope‑intercept form of a line? A: $y=mx+c$.

10. Q: Why is this exercise important? A: It helps visualize solutions and understand consistency of equations.

Conclusion

Exercise 3.2 has 10 solved questions and 10 FAQs that strengthen your understanding of graphical solutions of linear equations in two variables. This builds the foundation for algebraic methods in Class 10 Maths.

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