document.write( "Question 852545: What is the solution to the following systems of equations?\r
\n" ); document.write( "\n" ); document.write( " $\"y=2e%5E%282x%29\"$
\n" ); document.write( " $\"y=e%5Ex+-1\"$ \n" ); document.write( "

Algebra.Com's Answer #513470 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll take a shot at it
\n" ); document.write( " $\"y=2e%5E%282x%29\"$
\n" ); document.write( " $\"y=e%5Ex+-1\"$
\n" ); document.write( "----------------
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+2%2Ae%5E%282x%29+=+e%5Ex+-+1+\"$
\n" ); document.write( " $\"+2%2A%28e%5Ex%29%5E2+=+e%5Ex+-+1+\"$
\n" ); document.write( " $\"+2%2A%28e%5Ex%29%5E2+-+e%5Ex+%2B+1+=+0+\"$
\n" ); document.write( "Make the substitution:
\n" ); document.write( " $\"+z+=+e%5Ex+\"$
\n" ); document.write( " $\"+2z%5E2+-+z+%2B+1+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+z+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+2+\"$
\n" ); document.write( " $\"+b+=+-1+\"$
\n" ); document.write( " $\"+c=+1+\"$
\n" ); document.write( " $\"+z+=+%28+-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A2%2A1+%29%29+%2F+%282%2A2%29+\"$
\n" ); document.write( " $\"+z+=+%28+1+%2B-+sqrt%28+-7+%29%29+%2F+4+\"$
\n" ); document.write( " $\"+z+=+%28+1+%2B+7i+%29+%2F+4+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+z+=+%28+1+-+7i+%29+%2F+4+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "substituting again:
\n" ); document.write( " $\"+e%5Ex+=+%28+1+%2B+7i+%29+%2F+4+\"$
\n" ); document.write( " $\"+x+=+ln%28+1%2F4+%2B+%287%2F4%29%2Ai+%29+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+ln%28+1%2F4+-+%287%2F4%29%2Ai+%29+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "that's as far as I can go\r
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