Answer
Please see the graph.
Work Step by Step
$x^2+y^2 <9$
$x^2/9 – y^2/4 < 1$
$y > x-2$
$x^2+y^2 <9$ (green line)
$x^2/9 – y^2/4 < 1$ (orange line)
$y > x-2$ (blue line)
We can use the point $(1,1)$ to determine what sides of the lines to shade.
$x^2+y^2 <9$
$1^2+1^2 <9$
$1+1 < 9$
$2 < 9$ (true, so we shade the side of the line with this point)
$x^2/9 – y^2/4 < 1$
$1^2/9 – 1^2/4 < 1$
$1/9 – 1/4 < 1$
$4/4*1/9 -9/9*1/4 < 1$
$4/36 – 9/36 < 1$
$-5/36 < 1$ (true, so we shade the side of the line with this point)
$y > x-2$
$1 > 1-2$
$1 > -1$ (true, so we shade the side of the line with this point)
The solution of the system of equations is the overlap of these equations. For this solution, four points that are on the boundary are noted. The area between these four points is the solution area.
