Question

If the system of equations x+y=3, y+z=5 , z+x=4 , x+y+kz=6 is consistent, then k equals 
A) -1             B) 1               C) 2                  D) 0
the answer is option B please explain me as fast as you can 

Answer 1

Given that $x+y=3,y+z=5,z+x=4$ Therefore on adding it, we get $2(x+y+z)=12 .SOx+y+z=6$
Now put x+y=3 in above equation to get $3+z=6$ So z=3 Now, put value of x+y and z in the last given equation of ques, we get $x+y+kz=6. \\ 3+k(3)=6 \\ 3k=3 \\ k=1$