Question

do the equation 3x+6y=2 and 6x+12y=4 represent a pair of consistent lines ?

Answer 1

Hi ,

3x + 6y -2 = 0 ----( 1 )

6x + 12y - 4 = 0----( 2 )

Compare ( 1 ) and ( 2 ) with

a1x + b1y + c1 = 0,

a2 x + b2 y + c2 = 0 we get,

a1 = 3 , b1 = 6 , c1 = -2 ;

a2 = 6 , b2 = 12 , c2 = - -4

a1/a2 = 3/6 = 1/2

b1 / b2 = 6/12 = 1/2

c1 / c2 = ( -2 ) / ( - 4 ) = 1/2

Therefore ,

a1/a2 = b1/b2 = c1 / c2 = 1/2

Above system of equations are ,

dependent lines ,

Coincidendental lines .

Have infinitely many solutions.

I hope this helps you.

:)