LINEAR EQUATIONS IN TWO VARIABLES

LINEAR EQUATIONS IN TWO VARIABLES

1. TEST OF CONSISTENCY

   • IN A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES a1x+b1y+c1=0 a2x+b2y+c2=0
     • If a1 / a2 unequal to b1 / b2 ,the pair is consistent with a unique solution
     • If a1 / a2 = b1 / b1 unequal to c1 / c2 ,the pair is inconsistent
     • If a1/a2 = b1/b2 = c1/c2 ,then they are consistent with infinitely many solutions

2. GRAPHICAL REPRESENTATION

   • GRAPHICALLY A PAIR OF LINEAR EQUATIONS a1x +b1y+c1= 0 ; a2x+b2y+c2=0 REPRESENT A PAIR OF TWO STRAIGHT LINES
     • IF a1/a2 is unequal to b1 /b2 then the lines will intersect
     • IF a1/a2= b1/b2 unequal to c1/c2then the lines are parallel
     • if a1 / a2 = b1/ b2= c1/ c2, then the lines are coincident

3. SOLVING CASES IN ALGEBRIC METHOD

   • CROSS MULTIPLICATION METHOD
   • ELIMINATION METHOD
   • SUBSTITUTION METHOD

4. GENERAL FORM

   • a1x +b1y + c1= 0 ; a2x +b2y+c2=0 where a1, b1, c1, a2, b2 ,c2 ARE ALL REAL NUMBERS