Question

This circle and x + 2y= 12 create a system of equations.

Find all solutions, if any, of the resulting system
There are no solutions
(0,6) and (12, 0)
(0,5) and (12,0)
(0,5) and (5,0)

Answer 1

There's something wrong with the answer choices.

There are 2 solutions because the line x+2y = 12 and the circle intersect at two locations. One point of intersection is (0,6). So this suggests choice B is the answer; however, the point (12,0) is not a solution.

It works for x+2y = 12 since 12+2(0) = 12. But the point (12,0) is not on the circle. The furthest to the right we go is (6,0).