Answer
Please see the graph.
Work Step by Step
Blue line: $y\ge1$
Orange line: $x\lt-3$
To determine what sides of the lines to shade, we use a point not on the line. We can use (0,0) for the lines.
Blue line:
$y\ge1$
$0\ge1$ (false, so we shade above the line)
Orange line:
$x\lt-3$
$0\lt -3$ (false, so we shade the left side of the line)
The solution area is the overlap of the two inequalities.