For a pair of equations,if a_{1} b_{2}-a_{2} | vedclass

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(D) Given the equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$.The conditions provided are:$a_{1}b_{2} - a_{2}b_{1} = 0 \impl

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an infinite set

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(D) Given the equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$.The conditions provided are:$a_{1}b_{2} - a_{2}b_{1} = 0 \implies \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$$b_{1}c_{2} - b_{2}c_{1} = 0 \implies \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$$c_{1}a_{2} - c_{2}a_{1} = 0 \implies \frac{c_{1}}{c_{2}} = \frac{a_{1}}{a_{2}}$Combining these,we get $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = k$ (where $k$ is a constant).This implies that the two equations are dependent (coincident lines).For coincident lines,there are infinitely many solutions.Therefore,the solution set is an infinite set.

For a pair of equations,if $a_{1} b_{2}-a_{2} b_{1}=0, b_{1} c_{2}-b_{2} c_{1}=0$ and $c_{1} a_{2}-c_{2} a_{1}=0$,then the solution set of the pair of equations is ...........

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