Chapter 13, Problem 13CT

To determine

To find: the point of intersections of the lines.

Answer to Problem 13CT

The point of intersections of the lines is $\left(2,3\right)$ .

Explanation of Solution

Given information: The lines are $x+2y=8\&3x-y=3$ .

Calculation:

  $\begin{array}{l}x+2y=8\mathrm{......}\left(1\right)\\ 3x-y=3\mathrm{......}\left(2\right)\\ x=8-2y\mathrm{......}\left(3\right)\end{array}$

Put the value of $x$ in equation $\left(2\right)$ .

  $\begin{array}{l}3\left(8-2y\right)-y=3\\ 24-6y-y=3\\ -7y=3-24\\ -7y=-21\\ y=\frac{21}{7}\\ y=3\end{array}$

Put value of $y$ in equation $\left(3\right)$ .

  $\begin{array}{l}x=8-2y\\ x=8-2\left(3\right)\\ x=8-6\\ x=2\end{array}$