Boolean algebra problem simplification

Question

I am trying to simplify the following Boolean expression

$$xz + x'y + zy$$

and the solution said it was $xz + x'y$. How did they get this answer? Also, I found this on the MIT site.

Answer 1

$$xz + x'y + zy=\\ xz + x'y + zy(1)=\\ xz + x'y + zy(x+x')=\\xz + x'y + zyx+zyx'=\\ (xz + zyx)+( x'y +zyx')= \\xz(1+y)+x'y(1+z) $$ and you take over now