Question

The value of k for which the system of equations

x + 2y = 5

3x + ky + 15 = 0

has no solution is

A. 6

B. – 6

C. 3/2

D. None of these

Answer 1

Given:

Equation 1: x + 2y = 5

Equation 2: 3x + ky = – 15

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 no solutions we must have

According to the problem:

a₁ = 1

a₂ = 3

b₁ = 2

b₂ = k

c₁ = 5

c₂ = – 15

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

⇒ k = 6

Also we find

The value of k for which the system of equations has no solution is k = 6