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The system of equations shown is graphed on the coordinate plane. The graphs of the equations form a line and a parabola that intersect at two points.

y =- x + 3
y = x + 1
One point of intersection is (-2, -1). What are the coordinates of the other point?

User Chrisan
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1 Answer

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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).

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