NCERT Solutions Class 9 Maths Chapter 13 — Two Variables, One Line#
Chapter 13 (Ganita Manjari Part II) studies linear equations in two variables $ax + by + c = 0$: their solutions (ordered pairs), their graphs (straight lines), the slope of a line and the slope-intercept form $y = mx + c$. It then forms pairs of linear equations from real situations and solves them by substitution, elimination and graphs, using the ratios $\dfrac{a_1}{a_2}$, $\dfrac{b_1}{b_2}$, $\dfrac{c_1}{c_2}$ to tell whether the lines intersect, are parallel, or coincide.
exercise set 13.1
exercise set 13.2
exercise set 13.3
exercise set 13.4
exercise set 13.5
end-of-chapter exercises
Exercises#
- Exercise Set 13.1 — Standard form, coefficients and constant term; representing situations (3 questions)
- Exercise Set 13.2 — Solutions of a linear equation, quadrants, true or false (7 questions)
- Exercise Set 13.3 — Slope of hills, ramps and lines (4 questions)
- Exercise Set 13.4 — Framing pairs of linear equations (3 questions)
- Exercise Set 13.5 — Solving pairs of linear equations by substitution, elimination and graphs (9 questions)
- End-of-Chapter Exercises — Slope and intercepts, Celsius–Fahrenheit, mobile plans, coincident lines, robots, clocks and digits (14 questions)
What you will learn#
- Linear equations in two variables and their standard form $ax + by + c = 0$.
- Solutions of a linear equation, and its graph as a straight line.
- Slope and intercepts of a line.
- Framing pairs of linear equations and solving them by substitution, elimination and graphs.
Key formulas and results#
- Slope of a line $= \dfrac{\text{change in } y}{\text{change in } x}$.
- Two lines can meet in one point, be parallel (no solution) or coincide (infinitely many solutions).
Read and revise#
- NCERT Class 9 Maths Chapter 13 (PDF) — the Ganita Manjari Part II chapter itself.
- All Class 9 Maths chapters from Ganita Manjari Part I and Part II.
Frequently asked questions#
How many exercises are in Class 9 Maths Chapter 13?
Five exercise sets — 13.1 (3 questions), 13.2 (7 questions), 13.3 (4 questions), 13.4 (3 questions) and 13.5 (9 questions) — plus 14 end-of-chapter exercises. Every question is solved step by step here.
How many solutions does a linear equation in two variables have?
Infinitely many. Every point on its line is a solution. A pair of such equations usually has just one common solution — where the two lines cross.