Question

Write the condition for which the pair of liner

equations a1

x + b1

y + c1

= 0, a2

x + b2

y + c2

= 0

said to be inconsistent.
​

Answer 1

$\underline {\pink { Inconsistent \: system \:of \:linear \: equations : }}$

A system of linear equations in two variables is said to be inconsistent if it has no solution at all.

$If \: the \: system \:of \: linear \: equations \\a_{1}x + b_{1}y + c_{1} = 0 \:and \\a_{2}x + b_{2}y + c_{2} = 0 \: are \: \blue { inconsistent } \:then$

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

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