Term alignment in cases or array

Question

The MWE below shows the problem whether I uses the cases or array environment.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}

\[
\begin{cases}
\Phi^0_x\leqq 0, &{\Phi^{0}_x}'x_0=0,\\
\Phi_{z^*}^{0}\geqq 0, &{\Phi^{0}_{z^*}}'z_{0}^{*}=0.
\end{cases}
\]

\[
\left\{
\begin{array}{ll}
\Phi^0_x\leqq 0, &{\Phi^{0}_x}'x_0=0,\\
\Phi_{z^*}^{0}\geqq 0, &{\Phi^{0}_{z^*}}'z_{0}^{*}=0.
\end{array}
\right.
\]

\end{document}

In either case, I would like the inequalities on the left, and equalities on the right to line up. In addition, I would like the prime on the second line to match the prime on the first.

Answer 1

You can get away with alignedat.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}

\[
\left\{
\begin{alignedat}{3}
\Phi^0_x       &\leqq 0, &\qquad {\Phi^{0}_x}'    && x_0       &=0,\\
\Phi_{z^*}^{0} &\geqq 0, &\qquad {\Phi^{0}_{z^*}}'&& z_{0}^{*} &=0.
\end{alignedat}
\right.
\]

\[
\left\{
\begin{alignedat}{3}
\Phi^0_x       &\leqq 0, &\qquad (\Phi^{0}_x)'    && x_0       &=0,\\
\Phi_{z^*}^{0} &\geqq 0, &\qquad (\Phi^{0}_{z^*})'&& z_{0}^{*} &=0.
\end{alignedat}
\right.
\]

\end{document}

I added a second version with parentheses around the primed expressions: in the top instance, the prime appears to be hanging from nowhere.

Answer 2

Like this? In the amsldoc section 3.7 Alignment building blocks p.9

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{equation*}
    \left\{
    \begin{aligned}
        \Phi^0_x&\leqq 0, &{\Phi^{0}_x}'x_0&=0,\\
        \Phi_{z^*}^{0}&\geqq 0, &{\Phi^{0}_{z^*}}'z_{0}^{*}&=0.
        \end{aligned}
    \right.
\end{equation*}

\end{document}