Given:

Equation 1: x + 3y = 4 Equation 2: 2x + 6y = 7

Both the equations are in the form of :

a₁x + b₁y = c₁ & a₂x + b₂y = c₂ where

a₁ & a₂ are the coefficients of x

b₁ & b₂ are the coefficients of y

c₁ & c₂ are the constants

According to the problem:

a₁ = 1

a₂ = 2

b₁ = 3

b₂ = 6

c₁ = 4

c₂ = 7

Comparing the ratios of the coefficients we see:

⇒ …(i)

⇒ ⇒ …(ii)

⇒ …(iii)

On seeing equation (i), (ii) and (iii) we find

Conclusion: The system of linear equations has no solutions.

The given system of linear equations will have no solution for all values of x and y