SOLUTION: I need help with a problem. the directions are find all points of intersection. It is a problem our teacher made up but the problem is for our section for solving quadratic system

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Question 196069: I need help with a problem.
the directions are find all points of intersection. It is a problem our teacher made up but the problem is for our section for solving quadratic systems
equation 1-x^2+y^2+4x-6y+4=0
equation 2-x^2+y^2-4x-6y+12=0
Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
They look like circles. You can plot them here --> http://72.3.253.76/webMathematica3/quickmath/page.jsp?s1=graphs&s2=equations&s3=basic
When will they intersect? When they are equal to each other
So where is
x%5E2%2By%5E2%2B4x-6y%2B4+=+x%5E2%2By%5E2-4x-6y%2B12
4x+%2B+4+=+-4x%2B12
8x+=+8
x+=+1
Using that x and solving for y, yields y = 3
So they touch at one point (1,3)
Geogebra would be a good tool to plot these on one plot together.