SOLUTION: When finding a solution of system of equations, for a conic intersection, how do you know what to do when there is a question like {{{x^2 + y^2 = 16}}} and x + y = 2? I understand

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: When finding a solution of system of equations, for a conic intersection, how do you know what to do when there is a question like {{{x^2 + y^2 = 16}}} and x + y = 2? I understand       Log On


   

Question 553796: When finding a solution of system of equations, for a conic intersection, how do you know what to do when there is a question like x%5E2+%2B+y%5E2+=+16 and x + y = 2? I understand that on the second equation I need to get it to where y = -x - 2, but I dont understand how to plug it into the first equations to find the point.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
When finding a solution of system of equations, for a conic intersection, how do you know what to do when there is a question like x^2 + y^2 = 16 and x + y = 2? I understand that on the second equation I need to get it to where y = -x - 2, but I dont understand how to plug it into the first equations to find the point.
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x + y = 2
y=2-x
plug (2-x) for y in second equation
x^2 + y^2 = 16
x^2+(2-x)^2=16
x^2+4-4x+x^2=16
2x^2-4x-12=0
x^2-2x-6=0
Solve by following quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-2, c=-6
x=-(-2)±√[(-2)^2-4*1*(-6)]/2*1
x=2±√[28]/2
x=2±5.29/2
x=3.646
y=-1.646
or
x=-1.646
y=3.646
..