Q. 45.0( 5 Votes )

# The value of k fo A. 0

B. 2

C. 6

D. 8

Answer :

Given:

Equation 1: 3x + 5y = 0

Equation 2: kx + 10y = 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

According to the problem:

a_{1} = 3

a_{2} = k

b_{1} = 5

b_{2} = 10

c_{1} = 0

c_{2} = 0

__The equation will have a non zero solution only when it will satisfy a non trivial solution i.e. the equations should satisfy with values other than x = 0 & y = 0 .For the given system of equations the equation will have a non zero solution if__

.......(i)

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

### ⇒ 5k = 30 ⇒ k = 6

__The__ __value of k for which the system of equations has non zero solution is__ __k = 6__

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