PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1. GRAPHICAL REPRESENTATION

   • Infinitely many solutions (coincident lines ) i.e Dependent consistent
   • No solution i.e inconsistent (parallel lines)
   • Exactly one solution ( intersectiong lines) i.e consisstent (unique)

2. SOLUTION GRAPHICALLY

   • Each solution (x,y) corres[onds to a [oint on the line representiong the equation and vice versa

3. GENERAL FORM

   • a1x + b1y + c1 = 0 a2x + b2y + c2= 0

4. ALGEBRAIC METHODS

   • By substitution sovle : 7x-15y=2 and x+2y = 3 , substitute value of x in equation 7(3-2y0-15y = 2 => -29y= -19 +> y = 19/29 now from x= 3-2 (19/29) = 49/29
   • By elimination Solve : x+3y = 6 and 2x+3y=12 Now adding equation (i) and (ii) 3x=18 or x=6 Again from (i) x 2 -(i) and (ii) 3y =0. Hence x=6 and y=0

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