Question

What is the number of solutions of the pair of linear equation 4p-6q+18 = 0 and 2p-3q +9 = 0?​

Answer 1

Answer:

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Answer 2

Given : pair of linear equation 4p-6q+18 = 0 and 2p-3q +9 = 0  

To Find :  number of solutions

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)

4p-6q+18 = 0

2p-3q +9 = 0  

4/2  = - 6/-3  = 18/9

=> 2 = 2 = 2

Hence  infinite solutions and line coincide each other

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