Write the number of solutions of the following pair of linear equations:
x + 2y– 8 = 0
2x + 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:
⇒
⇒ …(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