Answer
Refer to the graph below.
Work Step by Step
Graph each inequality.
To graph $x^2+y^2\gt 1$, graph the circle $x^2+y^2=1$ using broken lines then shade the region outside the circle. (Refer to the blue graph below.)
To graph $\frac{x^2}{4}-y^2\ge 1$, graph the hyperbola $\frac{x^2}{4}-y^2=1$ then shade the region inside each curve. (Refer to the red graph below.)
The solution to the given system is the region that is common to both graphs, which is the graph of $\frac{x^2}{4}-y^2 \ge 1$.
Refer to the graph in the answer part above,
