When is a pair of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ is inconsistent?

Solution:

Given equations are: $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$

The given equations are consistent:

$( i)\. if\ \frac{a_1}{a_2}≠\frac{b_1}{b_2}$, th4e given equations have one unique solution.

Then, the given pair of equations is consistent with exact one solution.

$( ii)$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The given pair of equations have  infinite solution.

Then, given pair of equations is consistent with infinite solutions.

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Updated on: 10-Oct-2022

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