Hello, a4swe!

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: .