Question

Find the value of K for which the system of equation has no solution: 3x-y-5=0 6x-2y-k=0

Answer 1

3x-y-5=0                   1
6x-2y-k=0                 2
multiply equation 1 by 2
6x-2y-10=0               3
let's add equation 3 and equation 2
6x-2y-10+6x-2y-k=0
12x-10-k=0
12x=10+k
x=(10+k)/12
put it in equation 1
3(10+k)/12-y-5=0
(10+k)/4-y-5=0
(10+k)/4=y+5
10+k=4y+20
k=4y+20-10
k=4y+10
4y=k-10
y=(k-10)/4
put x and y value in 2
6(10+k)/12-2(k-10)/4-k=0
(60+6k)/12-(2k-20)/4-k=0
5+6k-2k+5-k=0
10+3k=0
3k=10
k=10/3