Question

Find the value of

k

for the following system of linear equations to have infinitely many solutions:
4x + (k-4)y = - 18
(k-4)x + y = 2k + 3

Answer 1

Answer:

Given that,

4x+(k-4)y=-18 and (k-4)x+y=2k+3

To which the equations have infinitely many solutions.

a1/a²=b1/b2=c1/c2

4/k-4=k-4/1

(k-4)²=4(1)

(k)²+(4)²-2(k)(4)=4

k²+16-8k=4

k²-8k+16-4=0

k²-8k+12=0

k²-6k-2k+12=0

k(k-6)-2(k-6)=0

k-2=0 or k-6=0

k=2 or k=6

when k=6 or k=2 the given equations have infinitely many solutions.