Question
Question
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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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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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Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
- 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.
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