question_answer

The pair of linear equations\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] in two variables represents a pair of straight lines which are intersecting if

A)  \[\frac{{{a}_{1}}}{{{a}_{2}}}\cancel{=}\frac{{{b}_{1}}}{{{b}_{2}}}\]

B)  \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\cancel{=}\frac{{{c}_{1}}}{{{c}_{2}}}\]

C)  \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]

D)  \[\frac{{{a}_{1}}}{{{a}_{2}}}\cancel{=}\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\]

Correct Answer: A

Solution :