Why do you need us to check it? It is just arithmetic.

If x= 1/2- a, y= -a, and z= a then the first equation becomes 2(1/2- a)+ 4(a)= 1- 2a+ a= 1- a. No, that is not correct so this is not a solution.

Or did you mean x= 1/(2-a), y=-a, z= a? In that case, 2x+ 4z= 2/(2- a)+ 4a which is still not 1.

No, sorry, your solution is not correct.