Question

In how many ways can two lines can be drawn in a plane?​

Answer 1

in 3 ways the two lines can be drawn in a plane

Answer 2

Given :  two lines in a plane

To Find : Number of ways   two lines can be drawn in a plane

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)

There are 3 ways , 2 lines in a plane can be drawn

1,  Lines are intersecting

2  Lines are Parallel

3  Lines are coinciding  

There are 3 ways , 2 lines in a plane can be drawn

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