Answer :

Given:

Equation 1: 2x + 3y = 5

Equation 2: 4x + ky = 10

Both the equations are in the form of :

a_{1}x + b_{1}y = c_{1} & a_{2}x + b_{2}y = c_{2} where

a_{1} & a_{2} are the coefficients of x

b_{1} & b_{2} are the coefficients of y

c_{1} & c_{2} are the constants

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

………(i)

According to the problem:

a_{1} = 2

a_{2} = 4

b_{1} = 3

b_{2} = k

c_{1} = 5

c_{2} = 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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