document.write( "Question 169252: I solved 48 problems but this one has me stumped and I have been working on it for 2hrs.
\n" ); document.write( "Solve the following system of nonlinear equations.
\n" ); document.write( "x^2 + y^2 = 3
\n" ); document.write( "x^2 + y = 0 \n" ); document.write( "

Algebra.Com's Answer #124790 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve the system of equations:
\n" ); document.write( "1) $\"x%5E2%2By%5E2+=+3\"$ This is a circle with its center at the origin and radius of $\"sqrt%283%29\"$ .
\n" ); document.write( "2) $\"x%5E2%2By+=+0\"$ This is a parabola that opens downard with its vertex at the origin.
\n" ); document.write( "Subtract equation 1) from equation 2) to get:
\n" ); document.write( " $\"y%5E2-y+=+3\"$ Subtract 3 from both sides.
\n" ); document.write( " $\"y%5E2-y-3+=+0\"$ Solve using the quadratic formula: $\"y+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ where: a = 1, b = -1, and c = -3
\n" ); document.write( " $\"y+=+%28-%28-1%29%2B-sqrt%28%28-1%29%5E2-4%281%29%28-3%29%29%29%2F2%281%29\"$
\n" ); document.write( " $\"y+=+%281%2B-sqrt%281-%28-12%29%29%29%2F2\"$
\n" ); document.write( " $\"y+=+%281%2B-sqrt%2813%29%29%2F2\"$
\n" ); document.write( " $\"y+=+%281%2Bsqrt%2813%29%29%2F2\"$ or $\"y+=+%281-sqrt%2813%29%29%2F2\"$ Now substitute these values of y, one-at-a-time, into either one of the two given equations to solve for x. Let's use equation 2)
\n" ); document.write( " $\"x%5E2%2By+=+0\"$ Subtract y from both sides.
\n" ); document.write( " $\"x%5E2+=+-y\"$ Substitute $\"y+=+%281%2Bsqrt%2813%29%29%2F2\"$
\n" ); document.write( " $\"x%5E2+=+-%281%2Bsqrt%2813%29%29%2F2\"$ Take the square root of both sides.
\n" ); document.write( " $\"x+=+sqrt%28-%281%2Bsqrt%2813%29%29%2F2%29\"$
\n" ); document.write( "So one solution is:
\n" ); document.write( "( $\"sqrt%28-%281%2Bsqrt%2813%29%29%2F2%29\"$ , $\"%281%2Bsqrt%2813%29%29%2F2\"$ ) \n" ); document.write( "

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