# Write the number of solutions of the following pair of linear equations:x + 2y– 8 = 02x + 4y = 16

Given:

Equation 1: x + 2y = 8 Equation 2: 2x + 4y = 16

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

The system of linear equations needs to be analyzed by checking the nature of ratios of each coefficients in the above two equations.

According to the problem:

a1 = 1

a2 = 2

b1 = 2

b2 = 4

c1 = 8

c2 = 16

Comparing the ratios of the coefficients we see:

### ⇒…(ii)

…(iii)

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

Conclusion: The system of linear equations have infinite number of solution.

The given system of linear equations will have infinite number of solutions for all values of x and y

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