Text Nodes not behaving nicely

With yshift=<value> you can manually adjust the child of the tree.

 documentclass[border=10pt,tikz]{standalone}
    usepackage[utf8]{inputenc}
    usepackage{graphicx}
    usepackage{tikz}
    usetikzlibrary{trees,positioning,shapes,shadows,arrows}
    begin{document}
    
    tikzset{
      basic/.style  = {draw, text width=2cm, drop shadow, font=sffamily, rectangle},
      root/.style   = {basic, rounded corners=2pt, thin, align=center, fill=white},
      level-2/.style = {basic, rounded corners=3pt, thin,align=left, fill=white, text width=7cm},
      level-3/.style = {basic, thin, align=center, fill=white, text width=1.8cm}
    }
    
    
    begin{tikzpicture}[
      level 1/.style={sibling distance=30em, level distance=5em},
    %   {edge from parent fork down},
      edge from parent/.style={->,solid,black,thick,sloped,draw}, 
      edge from parent path={(tikzparentnode.south) -- (tikzchildnode.north)},
      >=latex, node distance=1.2cm, edge from parent fork down]
      node[root] (A) at (0,2)  {$AX=0$};
      draw[->] (A) to (0,.3);
     node[root] {textbf{Always consistent}} 
      child {node[level-2] (c1) {textbf{rank $A=n$}  textbf{Unique Solution $X=0$}}}
      child {node[level-2,yshift=-6pt] (c1) {textbf{rank $A<n$}  textbf{Infinitely many Solutions  $n-r$ arbitrary parameters in solution}}};
    end{tikzpicture}  
    end{document}

Edit: added are code for the second tree diagram, definition for math operator ``rank`, a bit improved code.

With use of the forest package is simple:

documentclass[border=10pt, preview]{standalone}
usepackage{mathtools}            % <---
DeclareMathOperator{rank}{rank} % <---
usepackage[edges]{forest}
usetikzlibrary{arrows.meta,
                shadows}

begin{document}
    begin{forest}
for tree = {
% nodes
    draw, semithick,% rounded corners,
    minimum width = 4em, 
if level = 0{fill=orange!30}{fill = teal!30, text width=34mm},
    drop shadow,
    font = sffamilysmalllinespread{0.84}selectfont,
% tree
     grow = south,
   anchor = north,
    forked edge,        % for forked edge
    edge  = {-Stealth},
    s sep = 2mm,    % sibling distance
    l sep = 8mm,    % level distance
 fork sep = 4mm,    % distance from parent to branching point
            }
[$mathbf{AX=0}$,
    [Always consistent
        [{$rank(mathbf{A})=n$}      smallskip
         Unique Solution {$X=0$}]
        [{$rank(mathbf{A})<n$}      smallskip
         Infinitely many Solutions 
         $n-r$ arbitrary parameters 
         in solution]
    ]
]
end{forest}

medskip
    begin{forest}
for tree = {
% nodes
    draw, semithick,% rounded corners,
    minimum width = 4em,
if level = 0{fill=orange!30}{fill = teal!30, text width=34mm},
    drop shadow,
    font = sffamilysmalllinespread{0.84}selectfont,
% tree
     grow = south,
   anchor = north,
    forked edge,        % for forked edge
    edge  = {-Stealth},
    s sep = 2mm,    % sibling distance
    l sep = 8mm,    % level distance
 fork sep = 4mm,    % distance from parent to branching point
            }
[$mathbf{AX=B, B neq 0}$;
    [Consistent:  
     ${rank(mathbf{A})=rank(mathbf{A|B})}$
            [Unique Solution:  
             {$rank(mathbf{A})=n$}]
            [Infinity of Solutions: 
             {$rank(mathbf{A})<n$,}  
             $n-r$ arbitrary parameters in solution]
    ]       
    [Inconsistent:  
     $rank(mathbf{A})<rank(mathbf{A|B})$]
]
    end{forest}
end{document}

I am trying to give my own illustration with simple code. The texts rank A on the left and on the right are horizontally aligned.

documentclass[tikz,border=5mm]{standalone}
usepackage{amsmath,amssymb}
begin{document}
begin{tikzpicture}[>=stealth,thick]
defa{3}   
defb{1.8} 
path[nodes={draw,minimum width=4.5cm}]
(0,0) node[fill=yellow!50,minimum height=12mm,align=center] (H) {$mathbf{Ax=0}$[1mm]$mathbf{A}=mtimes n, mleqslant n, mathbf{x}inmathbb{R}^n$}
++(0,-b) node[fill=cyan!50,minimum height=8mm] (H1){Always consistent}
+(a,-1.5*b) node[fill=cyan!50,minimum height=22mm] (H2r){}
+(-a,-1.5*b) node[fill=cyan!50,minimum height=22mm] (H2l){}
;
path 
(H2r.north) node[below=1mm,align=left]{
    Infinitely many Solutions[2mm] 
    $r=text{rank}A<n$
    $n-r$ arbitrary 
    parameters in solutions}
(H2l.north) node[below=1mm,align=left]{
    Unique Solution[2mm] 
    $r=text{rank}A=n$
}
;

draw[->] (H)--(H1); 
draw[->] (H1)--++(0,-1)-|(H2r);
draw[->] (H1)--++(0,-1)-|(H2l);
end{tikzpicture}
end{document}