A) consistent
B) inconsistent
C) can't say
D) None of these
Correct Answer: B
Solution :
| The given pair of linear equations is |
| \[4x-5y-12=0\] and \[-8x+10y+20=0\] |
| On comparing with standard form of pair of linear equations, we get |
| \[{{a}_{1}}=4,\,{{b}_{1}}=-5,\,{{c}_{1}}=-12\] |
| and \[{{a}_{2}}=-8,\,{{b}_{2}}=10,\,{{c}_{2}}=20\] |
| Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{4}{-8}=-\frac{1}{2},\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-5}{10}=-\frac{1}{2}\] |
| and \[\frac{{{c}_{1}}}{{{c}_{2}}}=-\frac{12}{20}=-\frac{3}{5}\] |
| \[\because \,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| \[\therefore \] Given pair of linear equations is inconsistent. |
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