Answer
Please see the graph.
Work Step by Step
Red line: $y\le-x^2+3$
Blue line: $y\le2x-1$
We pick a point to determine what sides of the lines to shade. We pick $(5,0)$.
$(5,0)$
$y\le-x^2+3$
$0\le-5^2+3$
$0 \le -25+3$
$0 \le -22$ (false, so we shade the side of the line without this point)
$(5,0)$
$y\le2x-1$
$0\le2*5-1$
$0 \le 10-1$
$0 \le 9$ (true, so we shade the side of the line with this point)
The overlap of the two areas is the solution of the system of inequalities.
