Q. 63 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $57-64$, use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places.

$\left\{\begin{array}{l}xy=2\\ y=\ln x\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the system of equations is,

From the graph, the solution of the system is, $\left(2.35,0.85\right)$.

Step 1. Given information

$\left\{\begin{array}{l}xy=2\\ y=\ln x\end{array}\right.$

First we need to solve each equation for $y$.

Consider the first equation,

$$\begin{gathered} xy=2 \\ y=\frac{2}{x} \end{gathered}$$

The second equation is, $y=\ln \left(x\right)$.

Step 2 Now sketch a graph for the obtained equations.

In the graph, the two equations are intersecting at a point $\left(2.35,0.85\right)$. So, the system has only one solution.