A) \[3x-y=9,\,x-\frac{y}{3}=3\]
B) \[4x+3y=24,\,-2x+3y=6\]
C) \[5x-y=10,\,10x-2y=20\]
D) \[-2x+y=3,\,-4x+2y=10\]
Correct Answer: D
Solution :
| On comparing the above equations with standard form of pair of linear equations |
| \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\], |
| we get |
| [a] \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] as\[\frac{3}{1}=\frac{3}{1}=\frac{-9}{-3}\], consistent |
| [b] \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]as \[\frac{4}{-2}\ne -1\], consistent |
| [c] \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]as\[\frac{5}{10}=\frac{1}{2}=\frac{10}{20}\], consistent |
| [d] \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] as \[\frac{-2}{-4}=\frac{1}{2}\ne \frac{3}{10}\], inconsistent |
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