Chapter 7, Problem 6CT

To determine

Solve the given system of equation graphically

Answer to Problem 6CT

The system has one solution $\left(0.03,8.62\right)$ and $\left(1,12\right)$and graph is shown below

Explanation of Solution

Given:

The system of equations

  $\begin{array}{l}y–\ln x=\mathrm{12......}\left(1\right)\hfill \\ 7x–2y+11=–\mathrm{6.....}\left(2\right)\hfill \end{array}$

Consider the system of equations

  $\begin{array}{l}y–\ln x=\mathrm{12......}\left(1\right)\hfill \\ 7x–2y+11=–\mathrm{6.....}\left(2\right)\hfill \end{array}$

Use MAPLE to plot the graph of the equation (1) and (2)

Write the equations (1) and (2) in the rectangular box as follows

  $2x–3y=0,2x+3y=12$

Right click on the equation, go to plot and click on 2-D-Implicit plot.

The graphs of both equations are shown below

  

From the above graph, note that the lines intersect at only one point at $\left(0.03,8.62\right)$ and $\left(1,12\right)$

Hence, the system has one solution $\left(0.03,8.62\right)$ and $\left(1,12\right)$