1
Linear Equation Basics
Write equations in ax + by + c = 0 form and identify coefficients
Chapter route
Pair of Linear Equations in Two Variables
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2
Graphical Method
Generate ordered pairs to plot each line accurately
3
Graphical Method
Draw two lines on coordinate axes using suitable scale
4
Graphical Method
Identify intersection point as the common solution
5
Consistency
Recognise one solution when a pair of lines intersects
6
Consistency
Recognise no solution when a pair of lines is parallel
7
Consistency
Recognise infinitely many solutions when two equations represent same line
8
Algebraic Conditions
Apply a1/a2, b1/b2 and c1/c2 conditions for consistency
9
Substitution Method
Substitute one variable expression into another equation
10
Substitution Method
Select the easier equation or variable to isolate
11
Elimination Method
Eliminate one variable by adding or subtracting equations
12
Elimination Method
Multiply equations to make coefficients equal or opposite
13
Word Problems
Translate age, number, money and quantity situations into equations
14
Word Problems
Find unknowns and interpret them in the original context
15
Validation
Substitute answers back to verify correctness
16
Error Analysis
Catch wrong variable definitions, signs and unit mismatches
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