Chapter 13.3, Problem 4PSA

(a)

To determine

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

Answer to Problem 4PSA

There is no point of intersection.

Explanation of Solution

Given:

The given lines are:

  $\begin{array}{c}2x+y=10\left(1\right)\\ 8x+4y=17\left(2\right)\end{array}$

Calculation:

Multiplying equation $\left(1\right)$ by $4$ , the equation $\left(1\right)$ become $8x+4y=80$ , which is parallel to $\left(2\right)$ .

As the given two equations are parallel, so there is no point of intersection.

Therefore there is no point of intersection.

(b)

To determine

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

Answer to Problem 4PSA

The point of intersection is $\left(4,17\right)$ .

Explanation of Solution

Given:

The given lines are:

  $y=4x+1\left(1\right)$

The second given line is the line to the right of the $y$ -axis, parallel to it and $4$ units from it.

Calculation:

By the given condition the equation of second line is given as:

  $x=4\left(2\right)$

The point of intersection is calculated as:

  $\begin{array}{c}y=4\left(4\right)+1\left[\text{substitute}x=4\text{in equation}\left(1\right)\right]\\ y=17\end{array}$

Therefore the point of intersection is $\left(4,17\right)$ .