Chapter 3 · Question 1

What is a pair of linear equations in two variables? Write its general form and explain what a solution means.

Answer Revealed

Direct Answer:

A pair of linear equations in two variables has the form

a_1x+b_1y+c_1=0

and

a_2x+b_2y+c_2=0

. A solution is an ordered pair

(x,y)

satisfying both equations.

Two straight-line equations together form a pair. A solution is a point common to both lines.

The general pair is

a_1x+b_1y+c_1=0

and

a_2x+b_2y+c_2=0

, where

a_i,b_i,c_i

are real numbers and

a_i,b_i

are not both zero. The ordered pair

(x,y)

is a solution if substituting it makes both equations true. Graphically, it is a common point of the two lines.

A pair of linear equations in two variables has the form $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

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