How many solutions will the following systems of equations have?
x^2+y^2=10
x+y=4
a. infinite
b. 0
c. 1
d. 2
I'm thinking A. but I just want to make sure. If you have an answer that is different could you possibly show me how you got it, it would really help me prepare for my exam!
We have a circle and a straight line.
So, either the line intersects the circle in two points, or it is tangent at just one point, or it misses the circle entirely.
Since y = 4-x, plug that in to get
x^2 + (4-x)^2 = 10
x^2 + x^2 - 8x + 16 = 10
2x^2 - 8x + 6 = 0
Since b^2-4ac is positive, there are two solutions.
see the graphs at
http://www.wolframalpha.com/input/?i=plot+x^2%2By^2%3D10%2C+x%2By%3D4+