I'm not that good at math. determine the number of real solutions for each system of equations. system a has blank real solutions. system b has blank real solutions. system c has blank real solutions.

System A has ONE real solution

System B has NO real solutions

System C has ONE real solution

A is a circle around the origin and a line through the origin, so they'll intersect in two places; we can skip the detailed calculation.

B is the intersection of a parabola and a line; they can intersect in zero, one or two places depending on the details. Let's check

Discriminant,

Negative discriminant, zero real solutions for B.

System C is again a parabola and a line; we proceed similarly:

Zero discriminant, exactly one real solution for C.

this doesn't make sense lol