Equation (1) is a pair of intersecting lines; equation (2) is a circle.
. . They can intersect in (at most) four points.
Equation (1) give us two equations: .
Substitute (a) into (2): .
. . and we have two intersections: .
Substitute (b) into (2): .
. . which simplifies to the quadratic: .
. . which factors: .
. . and has roots: .
Substitute into (b) and we get: .
. . and we have two more intersections: .