Question

How many solutions exist for the system of equations graphed below?

mc011-1.jpg
none
one
two
infinitely many

Answer 1

I can’t see the image you mentioned. Could you upload the picture or describe the graphs (e.g., “two distinct lines that meet at one point,” “two parallel lines,” “a line and a circle intersecting at two points,” etc.)?

Meanwhile, here are quick rules you can use to decide:
- The number of solutions equals the number of intersection points of the graphs.
- Two distinct nonparallel lines → 1 solution.
- Two parallel distinct lines → 0 solutions.
- Two coincident (same) lines → infinitely many solutions.
- A line and a circle → 0, 1 (tangent), or 2 solutions depending on whether the line misses, is tangent to, or crosses the circle.
- Two circles → 0, 1 (tangent), or 2 solutions.

If you upload or describe the graph I’ll tell you which choice is correct.