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
• B. False

Answer 1

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 $\frac{a}{m}\ne \frac{b}{n}$

$2.$ System of linear equations is consistent with infinitely many solutions if $\frac{a}{m}=\frac{b}{n}=\frac{c}{d}$

$3.$ System of linear equations is inconsistent i.e it has no solution if $\frac{a}{m}=\frac{b}{n}\ne \frac{c}{d}$

In case 3. conditions becomes true i.e

$\frac{1}{2}=\frac{2}{4}\ne \frac{-4}{-12}$

$\frac{1}{2}=\frac{1}{2}\ne \frac{1}{3}$

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