In the pair of linear equations a_{1}x + b_{1 | vedclass

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(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$1$. If $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2

Vedclass · Accepted Answer

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Vedclass · Answer

(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$1$. If $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2}}$,the lines intersect at a single point,resulting in a unique solution.$2$. If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} 
eq \frac{c_{1}}{c_{2}}$,the lines are parallel,resulting in no solution.$3$. If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$,the lines are coincident,meaning they overlap at every point,resulting in infinitely many solutions.Therefore,the condition for infinitely many solutions is $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$.

In the pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$,then the system has infinitely many solutions.

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