Q. 65.0( 1 Vote )

For what value of k, the following pair of linear equations has infinitely many solutions?

10x + 5y – (k – 5) = 0

20x + 10y – k = 0

Answer :

Given:

Equation 1: 10x + 5y = (k – 5) Equation 2: 20x + 10y = k


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


For the system of linear equations to have infinitely many solutions we must have


………(i)


According to the problem:


a1 = 10


a2 = 20


b1 = 5


b2 = 10


c1 = k – 5


c2 = k


Putting the above values in equation (i) we get:


…(ii)


On solving the equality (ii) we get


5k = 10( k – 5 ) 5k = 10k – 50 5k = 50 k = 10


The value of k for which the system of equations has infinitely many solution is k = 10


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