Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables

1. Rules

   • a1, b1, c1, a2, b2, c2 must be real numbers
   • a1, b1, c1, a2, b2, c2 cannot be zero simultaneously

2. General Form

   • a1x+b1y+c1=0
   • a2x+b2y+c2=0

3. Solutions

   • 1) Algebracially
     • Algebraic Methods
       • By Substitution
       • By Elimination
       • By Cross-Multiplication
   • 2) Geometrically
     • Graphical Representation
       • Unique Solution
         • Intersecting Lines
       • Infinitely Many Solutions
         • Coincident Lines
       • No Solution
         • Parallel Lines
       • Equations for :-
         • x-axis: y=0
         • y-axis: x=0
         • Line Parallel to y-axis: x=constant
         • Line Parallel to x-axis: y=constant