Question

Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 5 to 5 and its y-axis ranges from negative 3 to 7, both in 1-unit increments. A parabola and a line are plotted. The line and parabola intersect at two points. 1 point of intersection is in quadrant 1 and the other is in quadrant 2.

Which of the following shows the solution(s) for this system of equations?

(1 point)
Responses

(0,8)
left parenthesis 0 comma 8 right parenthesis

(−3,0) and (3,0)
left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 3 comma 0 right parenthesis

There are no solutions.
There are no solutions.

(−2,4) and (2,4)
left parenthesis negative 2 comma 4 right parenthesis and left parenthesis 2 comma 4 right parenthesis
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Answer 1

To determine the solutions for the system of equations described, we need to consider the context of the problem, which mentions that a line and a parabola intersect at two points—one in quadrant 1 and the other in quadrant 2.

• Quadrant 1 has positive x and positive y coordinates.
• Quadrant 2 has negative x and positive y coordinates.

The choices provided are:

1. (0,8): This point lies in quadrant 1 (positive x and y).
2. (−3,0) and (3,0): These points lie on the x-axis, which is neither in quadrant 1 nor 2 since y=0.
3. There are no solutions: Since we know there are two intersection points, this option can be eliminated.
4. (−2,4) and (2,4): The point (−2, 4) is in quadrant 2 (negative x, positive y), and the point (2, 4) is in quadrant 1 (positive x, positive y).

Since the only option that provides intersection points in both quadrants is option 4:

(−2, 4) and (2, 4) are the solutions to the system of equations.