Question

Solution Sets of Simultaneous Equations Quick Check
4 of 54 of 5 Items





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

There are no solutions.
There are no solutions.

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

(−2,4) and (2,4)
left parenthesis negative 2 comma 4 right parenthesis and left parenthesis 2 comma 4 right parenthesis
Skip to navigation

Answer 1

Based on the information given about the intersections of a parabola and a line in a coordinate plane, there are two points of intersection: one in quadrant 1 (where \( x > 0 \) and \( y > 0 \)) and another in quadrant 2 (where \( x < 0 \) and \( y > 0 \)).

Let's evaluate the options against the criteria:

1. **(0,8)**: This point does not fit as it is not in quadrant 2.
2. **(−3,0) and (3,0)**: These points would be on the x-axis, which does not fulfill the requirement of being in quadrants 1 and 2 since both points have a y-coordinate of 0.
3. **(−2,4) and (2,4)**: This option fits the criteria: (−2, 4) is in quadrant 2, and (2, 4) is in quadrant 1.

Thus, the solution(s) for this system of equations is:

**(−2,4) and (2,4)**.