Question

Find the equation of line parallel to the y- axis and drawn through the point of intersection of $x-7y=-5and3x+y-7=0.$

Answer 1

The equation of any line through the point of interection of the given lines is of the form,
$x-7y+5k(3x+y-7)=0i.e.(1+3k)x+(k-7)y+5-7k=0$

IF this line is parallel to Y - axis, then the coefficeint of y should be zero,
i.e. $k-7=0\Rightarrow k=7$
On putting the value of k = 7 in Eq. (i), we get,
$(1+3\times 7)x+0+5-7\times 7=022x-44=0\therefore x-2=0,\text{Which is required equation.}$