Find the value of k such that the system of linear equations is inconsistent.

Question

Find the value of k such that the system of linear equations is inconsistent.

6x + 2y = 8
−9x + ky = −11

 

k=?

Answer 1

6x+2y=8

-9x+ky=-11

simplify eq1 by dividing all terms by 2

3x+y=4

multiply all terms of this equation by -3

-9x-3y=-12

-9x+ky=-11 (this is eq2)

if k=-3 the system will be inconsistent because you will have...

-9x-3y=-12

-9x-3y=-11

these lines are parallel and therefore have no solution

you also could have done the following..

6x+2y=8

2y=-6x+8

y=-3x+4

 

-9x+ky=-11

ky=9x-11

y=(9/k)x-(11/k)

(9/k)=-3

9=-3k

k=9/(-3)

k=-3