Answer
Please see the graph.
Work Step by Step
The red graph is a hyperbola, $ x^{2}-y^{2}\ge1$. The blue graph is $ x\ge0$.
Both graphs have greater than or equal to signs, so both graphs have solid lines. For only the red graph (the hyperbola), we pick three points to determine what parts of the graph to shade. We pick the points $(-2,0)$, $(0,0)$, and $(2,0)$. For the blue graph, we pick the point $(0,2)$.
$(-2,0)$
$x^{2}-y^{2}\ge1$
$(-2)^{2}-0^{2}\ge1$
$4 -0 \ge 1$
$4 \ge 1$ (true, so we shade the side of the graph with the point)
$(0,0)$
$x^{2}-y^{2}\ge1$
$0^{2}-0^{2}\ge1$
$0-0 \ge 1$
$0 \ge 1$ (false, so we shade the side of the graph without the point)
$(2,0)$
$x^{2}-y^{2}\ge1$
$(-2)^{2}-0^{2}\ge1$
$4 -0 \ge 1$
$4 \ge 1$ (true, so we shade the side of the graph with the point)
$x \ge 0$
$(0,2)$
$x \ge 0$
$0 \ge 0$
$0 \ge 0$ (true, so we shade the side of the graph with the point)
The overlap of the graphs is the solution set.
