What value of n, in these three simultaneous equations, will make the three equations have no solution?
nx + y = 1
ny + z = 1
x + nz = 1
Solution
Add the equations:
nx + 7 = 1
ny + = 1
x + nz = 1
nx + y + ny + z + x + nz = 3 (n+1)(x + y + z) = 3.
This can be true unless n = -1: (-1 + 1)(x + y + z) = 0(x + y + z) = 3? Nope.