Question

Find the combined equation of the pair of lines, both passing through the point $(-4,5)$ and parallel to the axes of co-ordinates.

Answer 1

Equation of a line parallel to $x-axis$ is $y=k$. This line passes through $(-4,5)$.

Hence, the equation is $y=5or(y-5)=0$ ......(1)

Equation of a line parallel to $y-axis$ is $x=k.$ This line passes $(-4,5)$.

Hence, the equation is $x=-4or(x+4)=0$ ......(2)
Hence, the joint or simultaneous equation of this pair of lines is
$(y-5)(x+4)=0,$
$xy-5x+4y-20=0.$