LINEAR EQUATIONS IN Two VARIABLES

LINEAR EQUATIONS IN Two VARIABLES

1. a1x+ b1y + c1 = 0 a2x+b2y + c2 = 0

   • Each solution (x , Y ) corresponds to a point on the line representing the equation and Visa Versa

2. Algebraic Methods of Solving linear Equations

   • Substitution Method
   • Cross Multiplication Method
   • Elimination Method

3. Comparing the ratios

   • GRAPHICAL REPRESENTATION Intersecting lines
     • a1 / a2 not equal to b1 / b2
       • EXACTLY ONE SOLUTION ( UNIQUE )
   • GRAPHICAL REPRESENTATION COINCIDENT LINES
     • a1/a2 = b1/ b2 = c1 / c2
       • INFINITELY MANY SOLUTIONS
   • REPRESENTATION GRAPHICAL PARALLEL LINES
     • a1/a2 = b1 / b2 not = to c1/ c2
     • No solution