A) \[a=2b\]
B) \[b=2a\]
C) \[a+2b=0\]
D) \[2a+b=0\]
Correct Answer: B
Solution :
| [b] The given pair of linear equation is |
| \[2x+3y-6=0\] and \[2ax+(a+b)y-24=0\] |
| Here, \[{{a}_{1}}=2,\,\,{{b}_{1}}=3,\,\,{{c}_{1}}=-6,\,\,{{a}_{2}}=2a,\,{{b}_{2}}=a+b,\,\,{{c}_{2}}=-24\]The given pair of linear equations has infinitely many solutions, if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\frac{2}{2a}=\frac{3}{a+b}=\frac{-6}{-24}\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\frac{1}{a}=\frac{3}{a+b}=\frac{1}{4}\,\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\frac{1}{a}=\frac{3}{a+b}\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,a+b=3a\,\,\,\,\Rightarrow \,\,b=2a\,\] |
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