Question

Show that the system of equations

`6x + 5y = 11, 9x + 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, `(a_1)/(a_2) = 6/9 = 2/3`

`(b_1)/(b_2) = 5/(15/2) = 2/3`

`(c_1)/(c_2) = (−11)/(−21) = 11/21`

Thus, `(a_1)/(a_2) = (b_1)/(b_2 )≠ (c_1)/(c_2)`, therefore the given system has no solution.