Class 9 Maths Chapter 4 Linear Equations in Two Variables – Exercise 4.3 NCERT Solutions

Introduction

Exercise 4.3 focuses on the graphical method of solving linear equations in two variables. You’ll learn how to plot equations on the Cartesian plane, identify intersection points, and interpret solutions visually.

Key Concept

• General Form:

$$$$ax+by+c=0

• Graphical Solution:

  • Plot both equations on the same plane.

  • Intersection point gives the solution $(x,y)$.

  • If lines are parallel → no solution.

  • If lines coincide → infinite solutions.

Solved Questions (Step by Step)

Q1. Plot $x+y=5$.

Solution:

• Rewrite: $y=5-x$.

• Points: $(0,5),(5,0)$.

• Plot these points and join to form a straight line.

Q2. Plot $x-y=3$.

Solution:

• Rewrite: $y=x-3$.

• Points: $(3,0),(4,1)$.

• Plot and join to form line.

Q3. Solve graphically: $x+y=5$, $x-y=3$.

Solution:

• Plot both lines.

• Intersection point = $(4,1)$.

• Solution: $x=4,y=1$.

Q4. Solve graphically: $2x+y=7$, $x-y=1$.

Solution:

• First line: points $(0,7),(3,1)$.

• Second line: points $(1,0),(2,1)$.

• Intersection = $(2,3)$.

Q5. Solve graphically: $3x+2y=12$, $x-y=2$.

Solution:

• First line: points $(0,6),(4,0)$.

• Second line: points $(2,0),(3,1)$.

• Intersection = $(\frac{8}{3},\frac{2}{3})$.

Q6. Plot $y=2x+1$.

Solution:

• Points: $(0,1),(1,3)$.

• Straight line through these points.

Q7. Plot $y=-x+4$.

Solution:

• Points: $(0,4),(4,0)$.

• Straight line through these points.

Q8. Solve graphically: $y=2x+1$, $y=-x+4$.

Solution:

• Intersection = $(1,3)$.

• Solution: $x=1,y=3$.

Q9. Solve graphically: $x+2y=6$, $2x-y=2$.

Solution:

• First line: points $(0,3),(6,0)$.

• Second line: points $(1,0),(2,2)$.

• Intersection = $(2,2)$.

Q10. Solve graphically: $x+y=10$, $x-y=4$.

Solution:

• Intersection = $(7,3)$.

Q11. Solve graphically: $2x+y=11$, $x-y=1$.

Solution:

• Intersection = $(4,3)$.

Q12. Solve graphically: $x+2y=7$, $2x-y=3$.

Solution:

• Intersection = $(\frac{9}{5},\frac{11}{5})$.

Q13. Solve graphically: $y=x$, $y=-x$.

Solution:

• Intersection = $(0,0)$.

Q14. Solve graphically: $y=3x$, $y=-x+2$.

Solution:

• Intersection = $(0.5,1.5)$.

Q15. Solve graphically: $y=4x$, $y=-2x+6$.

Solution:

• Intersection = $(1,4)$.

FAQs (10 for Exercise 4.3)

1. Q: What does graphical solution mean? A: Plotting equations and finding their intersection point.

2. Q: How many solutions can two linear equations have? A: One, none, or infinitely many.

3. Q: What if lines are parallel? A: No solution.

4. Q: What if lines coincide? A: Infinite solutions.

5. Q: How do you check solutions graphically? A: Intersection point satisfies both equations.

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

7. Q: What is the y‑intercept? A: Point where line crosses y‑axis.

8. Q: What is the x‑intercept? A: Point where line crosses x‑axis.

9. Q: Why is graphical method important? A: It gives a visual understanding of solutions.

10. Q: Can graphical method be used for more than two equations? A: Yes, but intersection of all lines must be checked.

Conclusion

Exercise 4.3 has 15 questions that strengthen your understanding of graphical solutions of linear equations. This visual approach helps you interpret solutions clearly and connects algebra with geometry.

Visit:www.fuzymathacademy.com