Chapter 13.3, Problem 6PSB

To determine

To find: The point of intersection of given two lines.

Answer to Problem 6PSB

The point of intersection is $\left(a,6-\frac{3}{2}a\right)$ .

Explanation of Solution

Given:

The given lines are:

  $\begin{array}{c}x=a\left(1\right)\\ 3x+2y=12\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}3\left(a\right)+2y=12\left[\text{substitute }x=a\text{in equation}\left(2\right)\right]\\ y=\frac{12-3a}{2}\\ y=6-\frac{3}{2}a\end{array}$

Therefore the point of intersection is $\left(a,6-\frac{3}{2}a\right)$ .