LINEAR EQUATIONS IN TWO VARIABLES

LINEAR EQUATIONS IN TWO VARIABLES

1. EQUATIONS FOR -

   • X-AXIS : Y=0
   • Y-AXIS: X=0
   • LINE PARALLEL TO X-AXIS Y = CONSTANT
   • LINE PARALLEL TO Y-AXIS X = CONSTANT

2. GENERAL FORM

   • a1x+b1y+c1=0 a2x+b2y+c2=0

3. RULES

   • a1,b1,c1,a2,b2,c2 MUST BE REAL NUMBERS
   • a1,b1 and a2,b2 CANNOT BE ZERO SIMULTANEOUSLY

4. SOLUTIONS

   • ALGEBRICALLY
   • GRAPHICALLY

5. GRAPHICAL REPRESENTATION

   • UNIQUE SOLUTION
     • INTERSECTING LINES
   • INFINITELY MANY SOLUTION
     • COINCIDENT LINES
   • NO SOLUTION
     • PARALLEL LINES

6. ALGEBRICAL REPRESENTATION

   • BY SUBSTITUTION
   • BY ELIMINATION
   • BY CROSS MULTIPLLICATION