Chapter 4 · Class IX Mathematics · NCERT Exercises

Linear Equations in Two Variables — Exercises

Graphing Lines & Infinitely Many Solutions — Both Exercises Solved

📂 2 Exercises 📝 6 Questions 🎓 Easy-Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 4.1

Linear equations in two variables; standard form ax+by+c=0; identifying a, b, c

2 Q Easy

②

Exercise 4.2

Solutions of linear equations; infinitely many solutions; graph of ax+by+c=0 is a straight line

4 Q Easy-Moderate

2 exercise files · 6 total questions

Chapter at a Glance

CBSE BoardsNTSE

6 Concepts

4 Formulas

Easy-Moderate Difficulty

5–6% Weightage

Before You Begin

Prerequisites

✓Linear equations in one variable (Class VIII)
✓Coordinate geometry — plotting points
✓Basic algebraic manipulation

Have Ready

🔧Graph paper
🔧Ruler
🔧Table of values template

Exercise Topic Map

Exercise 4.1 Rearrange to ax+by+c=0; identify coefficients a, b, c; confirm it is linear (degree 1)

Exercise 4.2 Find solutions by assigning x values; plot at least 2–3 points; join to get the line; note every point on the line is a solution

Key Formulae — Recall Before Solving

\(ax + by + c = 0,\quad a \ne 0 \text{ or } b \ne 0 \quad \text{(standard form)}\)

\(\text{Any } (x, y) \text{ on the graph satisfies the equation}\)

\(x = 0 \Rightarrow y = -c/b \quad \text{(y-intercept)};\quad y = 0 \Rightarrow x = -c/a \quad \text{(x-intercept)}\)

\(\text{Infinitely many solutions: a linear equation in 2 variables has infinite solution pairs}\)

NCERT Solving Method

Step 1 — Standard form: rearrange to ax+by+c=0; identify a, b, c clearly. Step 2 — Finding solutions: substitute any value for x; solve for y; create a table of at least 3 (x,y) pairs. Step 3 — Graph: plot the (x,y) pairs; join them with a straight line extending both sides; every point on this line is a solution. Step 4 — Special cases: x = k (vertical line, parallel to y-axis); y = k (horizontal line, parallel to x-axis). Step 5 — Class IX focus: do NOT find intersection of two lines — that is Class X; here, graph individual lines only.