document.write( "Question 38194: m^2 + 3n^2 = 11\r
\n" ); document.write( "\n" ); document.write( "m - n = 2\r
\n" ); document.write( "\n" ); document.write( "Conic - systems of two non-linear equations (two solutions) \r
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\n" ); document.write( "\n" ); document.write( "second question: y = x^2 and 7x = y + 12 (one solotion from these equations) \n" ); document.write( "
Algebra.Com's Answer #23701 by fractalier(6550)\"\" \"About 
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These are both solved the same way. We solve the linear equation and substitute for it into the curve...thus from
\n" ); document.write( "m^2 + 3n^2 = 11\r
\n" ); document.write( "\n" ); document.write( "m - n = 2
\n" ); document.write( "we have
\n" ); document.write( "m = n + 2
\n" ); document.write( "now substituting we get
\n" ); document.write( "(n + 2)^2 + 3n^2 = 11
\n" ); document.write( "n^2 + 4n + 4 + 3n^2 = 11
\n" ); document.write( "4n^2 + 4n - 7 = 0
\n" ); document.write( "This doesn't factor so use the quadratic and get
\n" ); document.write( "n = (-4 ± sqrt(128)) / 8
\n" ); document.write( "n = (-4 ± 8sqrt(2)) / 8
\n" ); document.write( "n = (-1 ± 2sqrt(2)) / 2
\n" ); document.write( "This gives you 2 values for n. To find each corresponding value of m, merely plug into m = n + 2 and you'll have your points of intersection.
\n" ); document.write( "The second problem is done the same way. \n" ); document.write( "
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