NCERT Solutions Class 10 Maths Chapter 3 — Pair of Linear Equations in Two Variables#

Chapter 3 covers methods of solving a pair of linear equations in two variables. You will learn to solve equations graphically and algebraically using the substitution method and the elimination method, and apply these to real-life word problems.

exercise 3.1 exercise 3.2 exercise 3.3

Exercises#

  • Exercise 3.1 — Graphical method and consistency of linear equations (7 questions)
  • Exercise 3.2 — Substitution method (3 questions)
  • Exercise 3.3 — Elimination method (2 questions)

What you will learn#

  • Draw the graphs of a pair of linear equations and read the solution from the point where the lines meet.
  • Tell from the ratios of the coefficients whether a pair has one solution, no solution or infinitely many.
  • Solve a pair of equations by substitution and by elimination.
  • Turn word problems on ages, fractions, speeds and prices into a pair of equations.

Key formulas and results#

  • For $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$: if $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$, the lines intersect and there is exactly one solution.
  • If $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$ but $\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$, the lines are parallel and there is no solution.
  • If all three ratios are equal, the lines coincide and there are infinitely many solutions.

Read and revise#

Frequently asked questions#

How many exercises are in Class 10 Maths Chapter 3?
Three: Exercise 3.1 (7 questions), Exercise 3.2 (3 questions) and Exercise 3.3 (2 questions) — 12 questions in all, each solved step by step here.
Which method should I use to solve a pair of linear equations?
Every method gives the same answer. Substitution is quickest when one variable has coefficient 1; elimination when the coefficients of one variable are equal or easy to make equal. Use the graph only when the question asks for it.

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