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