What are some fast ways to solve a system of 3 linear equations with this special form?

I have been thinking about whether there might be some faster way to solve a system of 3 linear equations with this form -

X + aY = b
Y + cZ = d
Z + eX = f

Note that every equation is missing a term, but that no two are missing the same term.

Since there are fewer terms than normal, I am thinking that there might be some faster way to solve these than a normal system of three linear equations, but I haven’t thought of any.

This is NOT homework.