A) \[-\frac{14}{3}\]
B) \[\frac{2}{5}\]
C) 5
D) 10
Correct Answer: D
Solution :
| The condition that system of linear equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] is inconsistent, if |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] ...(i) |
| Given system of linear equations are |
| \[x+2y=3\] or \[x+2y-3=0\] |
| and \[5x+ky+7=0\] |
| Here, \[{{a}_{1}}=1,\,{{b}_{1}}=2,\,{{c}_{1}}=-3\] |
| and \[{{a}_{2}}=5,\,{{b}_{2}}=k,\,{{c}_{2}}=7\] |
| From Eq. (i), we get |
| \[\frac{1}{5}=\frac{2}{k}\ne -\frac{3}{7}\] |
| Taking 1st and Und terms |
| \[\frac{1}{5}=\frac{2}{k}\Rightarrow k=10\] |
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