Q. 155.0( 3 Votes )

# If the system of equations kx – 5y = 2, 6x + 2y = 7 has no solution, then k =

A. – 10

B. – 5

C. – 6

D. – 15

Answer :

Given:

Equation 1: kx – 5y = 2

Equation 2: 6x + 2y = 7

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 no solutions we must have__

………(i)

According to the problem:

a_{1} = k

a_{2} = 6

b_{1} = – 5

b_{2} = 2

c_{1} = 2

c_{2} = 7

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

### ⇒ k ⇒ k = – 15

### Also we find

__The__ __value of k for which the system of equations has no solution is k = – 15__

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