A) \[y=3\]
B) \[y=-3\]
C) \[x+y=3\]
D) None of these
Correct Answer: A
Solution :
The equation of any line through the point of intersection of the lines\[x-y-1=0\]and\[2x-3y+1=0\]is \[(x-y-1)+\lambda (2x-3y+1)=0\] \[\Rightarrow \] \[(2\lambda +1)x-y(3\lambda +1)+(\lambda -1)=0\] ... (i) The line in Eq. (i) will be parallel to\[x-\], if it is of the form \[y=\]constant, therefore coefficient of\[x\]in Eq. \[(i)=0\] ie, \[2\lambda +1=0\Rightarrow \lambda =-\frac{1}{2}\] On putting\[\lambda =-\frac{1}{2}\]in Eq. (i), we get\[y=3\] This is the equation of the required line.
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