PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1. Algebraic Method

   • BY SUBSTITUTION Solve:7x-15y=2 eqn(1) x+2y=3 eqn(2) Solution:From eqn 2 , x=3-2y substitute value of x in equation (1) 7(3-2y)-15y=2 ,y=19/29 Now, from x=3-2y x=3-2(19/29)=(49/29)
   • BY ELIMINATION Solve:x+3y=6 eqn (1) 2x+3y=12 eqn (2) Now adding equation (1) and (2) 3x=18 or x=6 Again , from eqn (1)x2 -(2) 3y=0 or y=0 Hence x=6,y=0
   • BY CROSS MULTIPLICATION METHOD Solve :2x+3y-46=0 eqn (1) 3x+5y-74=0 eqn (2)

2. GENERAL FORM

   • a1x+b1y+c1=0 a2x+b2y+c2=0 a1,b1,c1,a2,b2,c2 are REAL NUMBERS

3. SOLUTION GRAPHICALLY

   • Each solution (x,y) corresponds to a point on the line representing the equation and vice-versa

4. GRAPHICAL REPRESENTATION

   • Pair of lines =x=2y-4=0 2x+4y-12=0 a1/a2=1/2,b1/b2=2/4,c1/c2=-4/-12 Comparing the ratios =a1/a2=b1/b2≠c1/c2 Algebraic interpretation :No solution -INCONSISTENT
   • Pair of lines =2x+3y-9=0 4x+6y-18=0 a1/a2=2/4,b1/b2=3/6,c1/c2=-3/-18 Compare the ratios =a1/a2=b1/b2=c1/c2 Algebraic Interpretation =Infinitely many solutions -Dependent
   • Pair of lines = x-2y=0 ,3x+4y-20=0 a1/a2=1/3,b1/b2=-2/4,c1/c2=0/-20 Compare the ratios =a1/a2≠ b1/b2 Algebraic Interpretation : Exactly one solution - consistent (unique)

Images and files in the map