hi everybody... I want to solve the following equations and search for x,y and z analytically while m and n are known

1)   x-y = 3*m-1

2)   z-x*y-y = 3*m^2-n^3

3)   z+x*z+x*n^3 = m^3

I know the answer is:

x=m+n-1; y=n-2m; z=m^2-nm-(n-1)*n^2;

I want to know the solution method:

I will appreciate any help