Question

find the value of variables in each
a, x-y+z =
b, x+2y-z = ​

Answer 1

a=x/(y−z)⇒x−ay+az=0

b=y/(z−x)⇒bx+y−bz=0

c=z/(x−y)⇒−cx+cy+z=0

since x,y,z are not all zero, the above system has a non-trivial solution. so,

Δ=0

⇒1+ab+bc+ca=0

∴ab+bc+ca=−1