System of quadratic equations with two uknowns

Question

solve for x and y:

(X-0.106)²+(y-0.106)²=0.41²

(X-0.3)²+(y-0.45)²=0.37²

Answer 1

Make note that you have a system of circle equations.  That is because they are in the form   (x-h)²+(y-k)²=r²

 

 

First, expand each equation using FOIL.

Second, isolate all the constant terms to one side and non-constant terms to the other side in both equations.

Third, use the elimination/substation method to solve for either x, x² , y, or y².  But in the end, we want to find x and y.  So try to reduce the amount of distinct variables as you can to get to that point.

 

 

 

An easier way would be to draw the 2 circles on the same coordinate system and find the points of intersection.