Q. 74.3( 3 Votes )

Write the number of solutions of the following pair of linear equations:

x + 2y– 8 = 0

2x + 4y = 16

Answer :

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:


…(i)



…(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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