Answer
0, 1, or 2 solutions
Work Step by Step
Please see the graphs. Let the ellipse (the red line) be $x^2/4 + y^2/9 = 1$.
The first two graphs (for no solutions and for one solution) are the first screenshot. The third graph (for two solutions) is the second screenshot.
For no solutions, let the blue line be the line $y=x+5$. The line doesn’t intersect the ellipse.
For one solution, let the blue line be the line $y=3$. The line intersects the ellipse at the point $(0,3)$.
For two solutions, let the blue line be the line $y=x$. The line intersects the ellipse at the points $(-1.664, -1.664)$ and $(1.664, 1.664)$.
