question_answer

Which one of the following statements is false for the following pair of linear equation?

\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]

\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]

A)  If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the line will be coincident

B)  If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are not equal, then the line will be intersecting

C)  If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are equal, then the line will be intersecting

D)  If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}},\] then the lines will be parallel

E)  None of these