Question

Check whether the following equations are consistent or inconsistent solve them graphically 4/3x+2y=8,2x+3y=12

Answer 1

Given : (4/3)x + 2y  = 8  2x + 3y  = 12  

To Find : following equations are consistent or inconsistent  

Solution:

a₁x + b₁y  = c₁

a₂x + b₂y = c₂

Consistent  if

a₁/a₂ = b₁/b₂ = c₁/c₂  ( Infinite solution , same line )

or  a₁/a₂ ≠ b₁/b₂   ( unique solution  , intersecting lines )

Inconsistent if

a₁/a₂ = b₁/b₂≠ c₁/c₂    ( no solution , Parallel lines)

(4/3)x + 2y  = 8  

2x + 3y  = 12  

(4/3)/2 = 2/3

2/3

8/12 = 2/3

2/3 = 2/3 = 2/3

( Infinite solution , same line )  

Consistent

Draw graph for both equation

Both  are same line.

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