Question

Find the equation of the x line parallel to the y-axis and drawn through the point of intersection of the lines $x-7y+5=0$ and $3x+y-7=0$

Answer 1

The equation of any line through the point of intersection of the given lines is of the form

$x-7y+5=0$ + k $3x+y-7=0$

$\Rightarrow (1+3k)x+(k-7)y+(5-7k)$ = 0

If the line is parallel to y-axis then coefficient of y should be 0, i.e., k - 7 = 0, which gives k = 7.

Substituting k = 7 in (i), we get : 22x - 44 = 0 $\therefore x-2=0$, which is the required equation.