Pair of Linear Equations in Two Variables

Vocabulary and key conceptual conditions for Class 10 Pair of Linear Equations in Two Variables including graphical and algebraic methods.

General form of a linear equation in two variables

$$ax + by + c = 0$$

Standard representation of a pair of linear equations

$a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$

Algebraic Methods of Solving

Substitution Method and Elimination Method

Condition for a Unique Solution

$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, which is Consistent and Independent

Condition for No Solution

$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$, which is Inconsistent and Independent

Condition for Infinite Number of Solutions

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, which is Consistent and Dependent

Graphical representation of No Solution

Two parallel lines that never intersect

Graphical representation of Infinite Solutions

Two lines that coincide (Line 1 and Line 2 are on top of each other)

Graphical representation of Unique Solution

Two lines that intersect at a single point

CBSE Chapter weightage

Total of $6$ Marks ($1$ mark - $1$, $2$ marks - $1$, $3$ marks - $1$)

Downstream

Movement of a boat in the same direction as the flow of the stream

Upstream

Movement of a boat against the direction of the flow of the stream

Inconsistent System

A system of equations that has no solution

Consistent and Dependent System

A system of equations that has an infinite number of solutions