$re = '/(?:\s+\$\s*(?P<in_line>[^$]+?)\s*\$\s+|^\s*\${2}\s*(?P<bloc>(?:[^$]{2})*?)\s*\${2})/m';
$str = 'Lorem ipsum dolor sit ame $ a = \\{ b, c \\} $ Lorem 100 \\$ ipsum
$$ \\left \\{
\\begin{array}{cl}y_1 =&3 x_1 - x_2 + x_3\\\\y_2 =&2 x_2\\\\y_3 =&x_1 - x_2 + 3 x_3\\end{array}
\\right.
\\Leftrightarrow \\left \\{
\\begin{array}{cl}8 x_1 =&3 y_1 + y_2 -y_3\\\\8 x_2 =&4 y_2\\\\8 x_3 =&-y_1 + y_2 + 3 y_3\\end{array}
\\right.
$$
Lorem ipsum dolor
$$ \\left \\{
\\begin{array}{cl}y_1 =&3 x_1 - x_2 + x_3\\\\y_2 =&2 x_2\\\\y_3 =&x_1 - x_2 + 3 x_3\\end{array}
\\right.
\\Leftrightarrow \\left \\{
\\begin{array}{cl}8 x_1 =&3 y_1 + y_2 -y_3\\\\8 x_2 =&4 y_2\\\\8 x_3 =&-y_1 + y_2 + 3 y_3\\end{array}
\\right.
$$
Lorem ipsum dolor $$$ Lorem ipsum dolor $$$. foo sit ame $ a = \\{ b, c \\} $ ';
preg_match_all($re, $str, $matches, PREG_SET_ORDER, 0);
// Print the entire match result
var_dump($matches);
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php