SOLUTION: Solve the following system of equations. x^2+y^2=34 y+2x=7

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Question 386346: Solve the following system of equations.
x^2+y^2=34
y+2x=7
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Since y = 7 - 2x, we can now substitute to obtain a quadratic expression in terms of x:
x%5E2+%2B+%287+-+2x%29%5E2+=+34

5x%5E2+-+28x+%2B+15+=+0

%285x+-+3%29%28x+-+5%29+=+0 (apparently, this luckily factors out)

x+=+5 or x+=+3%2F5

From this, we conclude y = -3 and y = 29/5, respectively. Checking, both of the ordered pairs satisfy both equations (they should, since a circle and a line normally intersect at two points).