Show that the system of equations 6x + 5y = 11, 9x + 15/2 y = 21

Question

Show that the system of equations 

6x + 5y = 11, 

9x + \(\frac{15}2\) y = 21

has no solution.

Answer 1

The given system of equations can be written as 

6x + 5y – 11 = 0 ….(i) 

⇒9x + 15/2 y - 21 = 0 …(ii) 

This system is of the form 

a₁x+b₁y+c₁ = 0 

a₂x+b₂y+c₂ = 0 

Here, a₁ = 6, b₁= 5, c₁ = -11 and a₂ = 9, b₂ = 15/2 , c₂ = -21 

Now,

therefore the given system has no solution.