Pair of Linear Equation in Two Variable

Pair of Linear Equation in Two Variable

1. General Form

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

2. Solution Graphically

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

3. Graphical Representation

   • No Solution, Inconsistent
     • Pair of Lines: x−y−6=0 2x−2y+2=0
       • a1/a2=b1/b2≠c1/c2
   • Infinitely many Solution, Consistent
     • Pair of Lines: 2x+y-1=0 4x+2y-2=0
       • a1/a2=b1/b2=c1/c2
   • Unique Solution,Consistent
     • Pair of Lines: 2x-y+1=0 x-2y+8=0
       • a1/a2≠b1/b2≠c1/c2

4. Algebric methods

   • By Substitution: Solve: 7x-15y=2 ----(i) x+2y=3 ----(ii) Solution: From eq (ii) substitute the value of x in eq (i) 7(3-2y)-15y=2 y=19/29. Now, from eq(ii),x-2(19/29)=3 x=49/29
   • By Elimination: Solve x+3y=6---(i) 2x+3y=12---(ii) Now,adding eq(i) and eq(ii); 3x=18 x=6. Again from (i)*2-(ii), y=0 . hence,x=6,y=0.

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