Question

Do the equation 4x+3y-1=5 and 12x+9y=15 represent a pair of coincident lines

Answer 1

No

this equation does not represent coincident line as:

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

$\frac{4}{3 } = \frac{3}{9} \: not \: equal \: to \: \frac{6}{15}$

thanks:)

Answer 2

Given : pair of equations 4x + 3y -1 = 5 and 12x + 9y = 15

To Find : Do the equation represent a pair of coincident lines

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

4x + 3y -1 = 5

=> 4x + 3y  = 6

12x + 9y = 15

4/12 = 3/9 ≠ 6/15

1/3 = 1/3  ≠ 2/5

Hence No solution  as  lines are parallel to each other

parallel lines

Lines does not represent  a pair of coincident lines

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