The question involves solving the given system of equations using graphing tools:

1. $xy = 8$
2. $y = \ln x$

To solve, the approach involves graphing both equations and identifying their points of intersection:

• Graph 1: $xy = 8$ is a hyperbolic equation.
• Graph 2: $y = \ln x$ is a logarithmic function, valid for $x > 0$.

The provided solutions are:

• Option A: $(4.98, 1.61)$
• Option B: There is no solution.

You attempted an answer including $(2.88, 2.88)$ and $(-2.88, -2.88)$, which may not align correctly with the equations due to the logarithmic function being undefined for negative $x$.

Would you like me to solve this algebraically or confirm the solution using numerical or graphical methods? Let me know if you'd like further details!

Related Questions to Explore:

1. How do hyperbolic equations interact with logarithmic equations graphically?
2. Can solutions for $y = \ln x$ exist for $x < 0$?
3. What techniques help to solve nonlinear systems of equations?
4. How can the intersections of $xy = k$ and $y = \ln x$ vary for different $k$?
5. How can you verify solutions graphically and algebraically?

Tip: Ensure proper domain checks (e.g., $x > 0$) when dealing with logarithmic equations!