Chapter 13.3, Problem 11PSB

To determine

To find: The point of intersection of give graphs of the two equations.

Answer to Problem 11PSB

The point of intersection is $\left(-1,2\right)$ .

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{c}y-3=\frac{1}{2}\left(x-1\right)\\ y+1=\frac{-3}{2}\left(x-1\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}\frac{1}{2}\left(x-1\right)+3=\frac{-3}{2}\left(x-1\right)-1\left[\text{put equation}\left(1\right)=\text{equation}\left(2\right)\right]\\ x+5=-3x-2\\ 4x=-4\\ x=-1\end{array}$

Further simplified as:

  $\begin{array}{c}y-3=\frac{1}{2}\left(-1-1\right)\left[\text{substitute }x=\text{2in equation}\left(1\right)\right]\\ y=2\end{array}$

Therefore the point of intersection is $\left(-1,2\right)$ .