PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1. GENERAL FORM

   • a1x+b1y+c1= 0, a2x+b2y+c2= 0 a1,b1,c1,a2,b2,c2: Real Numbers

2. Solution Graphically

   • Each solution (x, y) corresponds to a point on the line representing the equation and vice-versa.
   • Exactly one solution(intersecting lines) i.e. consistent(unique).
     • Infinitely many solutions(coincident lines) i.e. Dependent consistent.
       • No solution i.e. Inconsistent(parallel lines)

3. ALGEBRIC METHODS

   • ELIMINATION METHOD
     • Solve: x+3y= 6....(i) 2x-3y=12....(ii).
       • Solution: Now adding equations(i) and (ii) 3x= 18 or x= 6 again, from (i) and (ii) 3y=0 or y= 0.
   • SUBSTITUTION METHOD
     • Solve: 7x-15y= 2....(i) x+2y= 3....(ii)
       • Solution: From equation(ii), x= 3-2y substitute value of x in equation (i) 7(3-2y)-15y=2, y=19/29 Now from x=3-2y, x=3-2(19/29)= (49/29)