Question

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

Answer 1

The equation of any line parallel to the $y$-axis is of the form $x=a$......(1)

The two given lines are $x-7y+5=0$.....(2) and $3x+y=0$.....(3)

On solving equations (2) and (3) we obtain, $x=-\frac{5}{22}\text{and}y=\frac{15}{22}$

Therefore,$\{-\frac{5}{22},\frac{15}{22}\}$ is the point of intersection of lines (2) and (3)

since line $x=a$ passes through point $\{-\frac{5}{22},\frac{15}{22}\}$, $a=-\frac{5}{22}$

Thus, the required equation of line is $x=-\frac{5}{22}$