Answer
Please see the graph.
Work Step by Step
Red line: $x^2/4 + y^2 \leq1$
Blue line: $x + y >1$
The blue line will be dotted (since it uses a greater than sign), and the red line will be solid (since it uses a less than or equal to sign).
We pick the point $(0,0)$ to determine what sides of the graph to shade.
$x^2/4 + y^2 \leq1$
$0^2/4 + 0^2 \leq1$
$0/4 + 0 \leq 1$
$0 + 0 \leq 1$
$0 \leq 1$ (true, so we shade the side of the graph with this point)
$x+y>1$
$0 + 0 > 1$
$0 > 1$ (false, so we shade the side of the graph without the point)
The overlap of the two graphs is the solution set for the set of inequalities.
