Q. 35.0( 3 Votes )

# Write the value o

Answer :

Given:

Equation 1: 3x – 2y = 0

Equation 2: kx + 5y = 0

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} = 3

a_{2} = k

b_{1} = – 2

b_{2} = 5

c_{1} = 0

c_{2} = 0

In this problem since c_{1} & c_{2} = 0 so which is undefined.

__So for this problem__ __the system of linear equations will have infinite solutions if__

.......(ii)

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

### ⇒ – 2k = 15

### ⇒ k =

__The__ __value of k for which the system of equations has infinitely many solution is__ __k__ =

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