Multiple tagged equations on a singly tagged line

Question

I'm trying to build a way to have an arbitrary number of equations (typically two, but sometimes three, and if they're particularly short definitions even four) on a single line, but tagged only once on the right, individually.

I've been trying with minipages, as answered many times previously (like here and here).

I have two problems (EDIT: The first was solved in the comments):

1) The minipages add a small amount of whitespace, so their combined widths is larger than \linewidth:

Here's a MWE to show that some space is added. So the label (2) is to the right of label (3).

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{cleveref}

\newenvironment{splits}[1][0.5]{
\noindent\minipage{#1\linewidth}\align}
{\endalign\endminipage}

\begin{document}

\begin{splits}
x=0
\end{splits}
\begin{splits}
y=1
\end{splits}

\begin{align}
z=2
\end{align}

\end{document}

2) I cannot achieve the labelling only on the right-hand side. Labelling each equation is cluttered and out of place, but doing a \notag means I can't later do a \ref. What I would like, is something like (in the document above):

\begin{splits}[.25] \notag\label{1}
x=0
\end{splits}
\begin{splits}[.25] \notag\label{2}
y=1
\end{splits}
\begin{splits}[.25] \notag\label{3}
z=2
\end{splits}
\begin{splits}[.25]
\tag*{\cref{1,2,3}}
\end{splits}

With the idea being output that has looks like:

x=1        y=2        z=3        (1-3)
x_1=1      x_2=2      z_3=3    (1 a-c)

The exact content of the label isn't so important, so it could be (1a-1c) or something similar.

Answer 1

Is it something like this you want? I redefined your splits environment with tabularx:

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tabularx}
 \usepackage{cleveref}

\newenvironment{splits}[1][2]{
\vspace{\abovedisplayshortskip}\par\centering\tabularx{\linewidth}{*{#1}{>{\equation}X<{\endequation}}}}
{\endtabularx\vspace{\dimexpr\belowdisplayshortskip-\belowdisplayskip}\par}

\begin{document}
Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text.%

 \begin{splits}[3]
x=0 \label{eq-a} & y=1 \label{eq-b} & z=2 \label{eq-c}
 \end{splits}%
See \cref{eq-b,eq-s3}. Some more text. Some more text. Some more text.
\begin{subequations}
 \begin{splits}[3]
x=0 \label{eq-s1} & y=1 \label{eq-s2} & z=2 \label{eq-s3}
 \end{splits}%
 \end{subequations}

\end{document}