document.write( "Question 387221: Can you help me solve this system? x^2+y^2=4 and y=x^2-2 \n" ); document.write( "

Algebra.Com's Answer #275918 by robertb(5830) $\"\"$ $\"About$

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$\"+x%5E2%2By%5E2=4+\"$ and $\"y=x%5E2-2\"$ .
\n" ); document.write( "The 2nd equation becomes $\"y+%2B+2=x%5E2\"$ . Substitute.
\n" ); document.write( " $\"y%5E2+%2B+y+%2B+2+=+4\"$ , or $\"y%5E2+%2B+y+%2B+-2+=+0\"$ .
\n" ); document.write( "(y+2)(y - 1) = 0.
\n" ); document.write( "y = -2, y = 1. When y = -2, then $\"-2+%2B+2+=+x%5E2\"$ , so x = 0.
\n" ); document.write( "When y = 1, then $\"1%2B2+=+x%5E2\"$ , or $\"x%5E2+=+3\"$ , or x = $\"-sqrt%283%29\"$ , $\"sqrt%283%29\"$ . Therefore there are 3 solutions: ( $\"-sqrt%283%29\"$ , 1), ( $\"sqrt%283%29\"$ , 1), and (0, -2). The solutions correspond to the 3 points of intersection of the parabola $\"y=x%5E2-2\"$ and the circle $\"+x%5E2%2By%5E2=4+\"$ . \n" ); document.write( "

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