Linear Equations with two Variables

Linear Equations with two Variables

1. Equations for :

   • x- axis : y=0
   • y-axis : x= 0
   • Line parallel to y-axis : x=constant
   • Line parallel to x-axis : y=constant

2. General form :

   • a1x+b1y+c1 = 0
   • a2x+b2y+c2 = 0

3. Rules :

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

4. Solutions :

   • algebraically and Graphically

5. Graphical Representation

   • Unique Solutions
     • Intersecting Lines
   • Infinitely many solutions
     • Coincident Lines
   • No solution
     • Parallel lines

6. Algebraic methods

   • By substitution
   • By Elimination
   • By Cross-multiplication