5. In the xy-plane, which of the following are the coordinates of the point of intersection for the system of equations given above?
Answer: B
(3ln2,8)
The coordinates of the point of intersection for the system of equations are (3ln2, 8), which indicates where the two equations meet in the xy-plane.
A) (1,8)
This option is incorrect because substituting x = 1 into the equations will not yield a valid intersection point. The y-coordinate does not satisfy both equations simultaneously.
B) (3ln2,8)
This option is correct as substituting x = 3ln2 into both equations results in y = 8. This confirms that (3ln2, 8) is the point where the two equations intersect.
C) (8,8)
This option is incorrect because substituting x = 8 into the equations does not satisfy both equations. Therefore, it cannot be the point of intersection.
D) (8ln2,8)
This option is also incorrect. When substituting x = 8ln2 into the equations, the corresponding y value does not equal 8, indicating that this point does not satisfy both equations.
Conclusion
The correct answer, (3ln2, 8), is the only point that satisfies both equations in the system, confirming it as the intersection point. All other options fail to meet the conditions set by the equations, making them invalid choices.