A) coincident
B) parallel
C) intersecting exactly at one point
D) perpendicular to each other
Correct Answer: C
Solution :
| [c] The given pair of linear equations are |
| \[2x+3y-2=0\] and \[x-y-5=0\] |
| Here, \[{{a}_{1}}=2,\,{{b}_{1}}=3,\,{{c}_{1}}=-2,\,\,{{a}_{2}}=1,\,{{b}_{2}}=-1,\,{{c}_{2}}=-5\] |
| Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{1}=2,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{-1}=-3\Rightarrow \frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] |
| \[\therefore \] The given lines are intersecting exactly at one point. |
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