# The lines 2 x − y = 4 and 6 x − 2 y = 10 are not parallel and also find their point of intersection.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 41E
To determine

## To show: The lines 2x−y=4 and 6x−2y=10 are not parallel and also find their point of intersection.

Expert Solution

The point of the intersection is (1,2).

### Explanation of Solution

Formula used:

The non-vertical lines are parallel if and only if they have the same slope. That is, m1=m2.

Calculation:

It is enough to show that m1=m2, in order to say the two lines are parallel.

Find the slope of the line 2xy=4 as follows.

y=42x

y=2x4. (1)

Therefore, the slope is m1=2.

Find the slope of the line 6x2y=10 as follows.

2y=106xy=53x

y=3x5. (2)

Therefore, the slope is m2=3.

Here, m1m2.

From the given formula, the given two lines are not parallel.

Hence, it is proved that the lines 2xy=4 and 6x2y=10 are not parallel.

In order to find the intersection of their points, equate the equations (1) and (2) as follows.

2x4=3x52x3x=5+4x=1x=1

Now substitute x=1 in either 2xy=4 or 6x2y=10.

2(1)y=42y=4y=42y=2

Therefore, the point of the intersection is (1,2).

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