It sort of depends on what PQ and PS are and, you have not bothered to provide that information!
Then they are simultaneous equations.
Invisible lines!
What do you call equations describing two or more lines
That they, along with the equations, are invisible!
They are simultaneous equations.
Since rs is the perpendicular bisector of pq, it follows that point s is the midpoint of segment pq, meaning that ps is equal to qs. Additionally, because rs is perpendicular to pq, the angles formed at the intersection (∠prs and ∠qrs) are both right angles (90 degrees). Consequently, any point on line rs is equidistant from points p and q.
sd ad ps fd
Its called Simultaneous Equations
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
For vertical lines, when you try to figure out the slope, you get zero in the denominator - in other words, a division by zero.
The coordinates of the point of intersection must satisfy the equations of both lines. So these coordinates represent the simultaneous solution to the two equations that that represent the lines.