Answer :


Equation 1: 2x + 3y = 5

Equation 2: 4x + ky = 10

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


According to the problem:

a1 = 2

a2 = 4

b1 = 3

b2 = k

c1 = 5

c2 = 10

Putting the above values in equation (i) and solving the extreme left and middle portion of the equality we get the value of k

2k = 12 k = 6

Also we find

The value of k for which the system of equations has infinitely many solution is k = 6

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