Final answer:
The system of equations consists of a line and a parabola on the coordinate plane, intersecting at two points. One point is given as (-2, -1), and by solving the system algebraically, the other point of intersection is found to be (1, 2).
Step-by-step explanation:
The student is provided with two equations forming a system: y = -x + 3 and y = x^2 + 1, which represent a line and a parabola on the coordinate plane, respectively. We are given that one point of intersection between the line and the parabola is (-2, -1). To find the other point of intersection, we can set the two equations equal to each other because at the points of intersection, the y-values must be the same.
Let's solve the system:
Set the equations equal: -x + 3 = x^2 + 1.
Rearrange the terms: x^2 + x - 2 = 0.
Factor the quadratic equation: (x + 2)(x - 1) = 0.
Determine the roots: x = -2, x = 1.
Find the corresponding y-values for each x by substituting back into any of the original equations. For x = 1, y = -x + 3 gives us y = 2.
The coordinates of the second point of intersection are therefore (1, 2).