Answer :

Given:

Equation 1: x + 2y = 5


Equation 2: 3x + ky = – 15


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 no solutions we must have


………(i)


According to the problem:


a1 = 1


a2 = 3


b1 = 2


b2 = k


c1 = 5


c2 = – 15


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



k = 6


Also we find


The value of k for which the system of equations has no solution is k = 6

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