Answer
Please see the graph.
Work Step by Step
Red line: $2x+5y \geq 10$
Blue line: $y\geq x^2+1$
We pick the point $(0,0)$ to determine what sides of the graphs to shade. Since both lines have greater than or equal to signs, we will have solid lines.
$2x+5y \geq 10$
$2*0+5*0 \geq 10$
$0 + 0 \geq 10$
$0 \geq 10$ (false, so we shade the side of the graph without the point)
$y \geq x^2+1$
$0 \geq 0^2+1$
$0 \geq 0 + 1$
$0 \geq 1$ (false, so we shade the side of the graph without the point)
The overlap of the two graphs is the solution set to the set of inequalities.
