How do you solve the system #x^2+y^2=9# and #x-3y=3#?
1 Answer
There are two solutions to this system: the points
Explanation:
This is an interesting system of equations problem because it yields more than one solution per variable.
Why this happens is something we can analyze right now. The first equation, is the standard form for a circle with radius
So naturally if we consider that a solution to this system will be a point where the line and the circle intersect, we should not be surprised to learn that there will be two solutions. One when the line enters the circle, and another when it leaves. See this graph:
graph{(x^2 + y^2 - 9)((1/3)x -1-y)=0 [-10, 10, -5, 5]}
First we start by manipulating the second equation:
We can insert this directly into the first equation to solve for
Obviously this equation has two solutions. One for
Now we can solve for the
If
If
So our two solutions are the points: