Find the equation of the line parallel to y-axis and drawn through


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


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)

3x + y = 0 … (3)

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

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

Since line $x=$ a passes through point $\left(-\frac{5}{22}, \frac{15}{22}\right), a=-\frac{5}{22}$.

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

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