In the xy-plane, which of the following are the coordinates of the point of intersection for the system of equations given above?

Rationale

(3ln2,8)

The point of intersection for the given system of equations is determined by solving both equations simultaneously, which results in the coordinates (3ln2, 8). This point satisfies both equations, confirming it as the correct solution.

A ((1,8)) YOUR ANSWER

This coordinate does not satisfy both equations in the system. While it has a y-coordinate of 8, substituting x = 1 into the equations reveals that it does not meet the required conditions for intersection, thus it cannot be the point of intersection.

B ((3ln2,8)) CORRECT

This is the correct choice, as substituting x = 3ln2 into both equations yields the same y-coordinate of 8, confirming that this point is indeed the intersection of the two lines represented by the equations.

C ((8,8)) YOUR ANSWER

Although this point has a y-coordinate of 8, substituting x = 8 into the equations shows that it does not satisfy both equations. Therefore, it cannot be the point of intersection, as it does not lie on both lines.

D ((8ln2,8)) YOUR ANSWER

Similar to the previous choices, this point does not satisfy both equations in the system. Substituting x = 8ln2 results in a different y-coordinate than 8 for at least one of the equations, meaning it cannot be the intersection point.

Conclusion

The coordinates (3ln2, 8) represent the unique solution where both equations intersect in the xy-plane. The other choices fail to satisfy the equations, confirming that they do not represent the point of intersection. Understanding these intersections is crucial in systems of equations, as they illustrate the relationships between linear expressions graphically.

In the xy-plane, which of the following are the coordinates of the point of intersection for the system of equations given above?

(3ln2,8)

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