Question

the lines representing the equations a1x+b1y+c1=0 and a2x+b2y+c2=0 is as shown in the fig.write the mathematical relation among a1,a2,b1,b2,c1,and c2​

Answer 1

Given :  the lines representing the equations a1x+b1y+c1=0 and a2x+b2y+c2=0  

To Find : the mathematical relation among a1,a2,b1,b2,c1,and c2​

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)

As fig  is missing  : answer will depend upon figure

If Lines are intersecting then :

a₁/a₂ ≠ b₁/b₂

If Lines are parallel then :

a₁/a₂ = b₁/b₂ ≠  c₁/c₂

If lines are coincident then

  a₁/a₂ = b₁/b₂ = c₁/c₂

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Answer 2

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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)

As fig is missing : answer will depend upon figure

If Lines are intersecting then :

a₁/a₂ ≠ b₁/b₂

If Lines are parallel then :

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

If lines are coincident then

a₁/a₂ = b₁/b₂ = c₁/c₂