Chapter 13.3, Problem 3PSA

(a)

To determine

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

Answer to Problem 3PSA

The point of intersection is $\left(12,0\right)$ .

Explanation of Solution

Given:

The given lines are:

  $\begin{array}{l}x+2y=12\left(1\right)\\ x\text{-axis}\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}y=0\left[\text{as the given line is}x\text{-axis}\right]\\ x+2\left(0\right)=12\left[\text{substitute }y=0\text{ in equation }\left(1\right)\right]\\ x=12\end{array}$

Therefore the point of intersection is $\left(12,0\right)$ .

(b)

To determine

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

Answer to Problem 3PSA

The given two lines has no point of intersection.

Explanation of Solution

Given:

The given lines are:

  $\begin{array}{c}y=3x-7\left(1\right)\\ 9x-3y=21\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}3y=9x-21\left[\text{multiplying equation }\left(1\right)\text{ by 3}\right]\\ 9x-3y=21\left(3\right)\end{array}$

Equation $\left(3\right)$ shows that the given two lines are equivalent, so there are infinitely many solutions.

Therefore the given two lines has infinitely many point of intersection.