NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 7

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 7

Question:

Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the rails cross each other?

Given:

Equation of rail 1: x + 2y – 4 = 0

Equation of rail 2: 2x + 4y – 12 = 0

To Find:

Whether the two rails cross each other.

Formula:

If two lines are represented by the equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then the lines are parallel if a1a2 = b1b2.

Solution:

Let the given equations be

x + 2y – 4 = 0 .....(1)

2x + 4y – 12 = 0 .....(2)

From equation (1), we have x = 4 - 2y

Substituting this in equation (2):

2(4 - 2y) + 4y – 12 = 0

⇒ 8 – 4y + 4y – 12 = 0

⇒ –4 = 0

This is a contradiction.

Alternatively, we can check if the lines are parallel:

For equation (1): a1 = 1, b1 = 2

For equation (2): a2 = 2, b2 = 4

a1a2 = 12 = 12

b1b2 = 24 = 12

Since a1a2 = b1b2, the lines are parallel.

Result:

The rails are parallel and hence will not cross each other.

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