Systems are not “mixtures” of one or the other. The existence of Private Property does not mean the system is Capitalist, nor does the existence of Public Property mean the system is Socialist. Capitalism and Socialism are used to describe which is dominant in the overall system, guiding its trajectory. Per Engels:

Question 17 : Will it be possible to abolish private property at one stroke?

Answer : No, no more than the existing productive forces can at one stroke be multiplied to the extent necessary for the creation of a communal society. Hence, the proletarian revolution, which in all probability is approaching, will be able gradually to transform existing society and abolish private property only when the necessary means of production have been created in sufficient quantity.