On comparing the ratios a1/a2,b1/b2 and c1/c2 , find out whether the following pair of linear equations are consistent, or inconsistent.

(i) 3x + 2y = 5, 2x − 3y = 7

Comparing equation 3x + 2y = 5 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

Therefore,these linear equations will intersect at one point only and have only one possible solution.
And,pair of linear euations is consistent

(ii) 2x − 3y = 8, 4x − 6y = 9

Comparing equation 2x − 3y = 8 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

We get,

Therefore,these linear equations are parallel to each other and have no possible solution.in
And,pair of linear euations is inconsistent

(iii) 3x/2 + 5y/3 = 7, 9x − 10y = 14

Therefore, these linear equations will intersect each other at one point and have only one possible solution.
And,pair of linear euations is consistent

(iv) 5x − 3y = 11, −10x + 6y = −22

Comparing equation 5x − 3y = 11 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

We get,

Therefore these pair of lines have infinite number of solutions
And,pair of linear euations is consistent