Years ago I found this solution to typeset systems of equation within Mathematica:
Grid[{{PasteButton[
DisplayForm[
StyleBox[
RowBox[{StyleBox["{", SpanMaxSize -> \[Infinity]],
GridBox[{{"\[Placeholder]"}, {"\[Placeholder]"}},
ColumnAlignments -> Left]}], ShowAutoStyles -> False]]],
PasteButton[
DisplayForm[
StyleBox[
RowBox[{StyleBox["{", SpanMaxSize -> \[Infinity]],
GridBox[{{"\[Placeholder]"}, {"\[Placeholder]"}, {"\
\[Placeholder]"}}, ColumnAlignments -> Left]}],
ShowAutoStyles -> False]]],
PasteButton[
DisplayForm[
StyleBox[
RowBox[{StyleBox["{", SpanMaxSize -> \[Infinity]],
GridBox[{{"\[Placeholder]"}, {"\[Placeholder]"}, {"\
\[Placeholder]"}, {"\[Placeholder]"}}, ColumnAlignments -> Left]}],
ShowAutoStyles -> False]]]}}, Spacings -> 0]