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Question

State whether true or false.
The path of a train A is given by the equation x+2y−4=0 and the path of another train B is given by the equation 2x+4y−12=0. Train A and train B cross at some point.

A
True
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B
False
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Solution

The correct option is B False
Using conditions of consistency for linear equations ax+by+c=0 and mx+ny+d=0 we have :

1. System of linear equations is consistent with unique solutions if ambn

2. System of linear equations is consistent with infinitely many solutions if am=bn=cd

3. System of linear equations is inconsistent i.e it has no solution if am=bncd
In case 3. conditions becomes true i.e

12=24412

12=1213

given linear equation has no solution which implies that train A and train B will not cross each other at any point.

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