document.write( "Question 252412: I have been sitting here for hours trying to figure the following problems. I am working on Non-Linear Systems and have to solve the following systems. No matter how I work it I can't seem to come to a solution.\r
\n" ); document.write( "\n" ); document.write( "1) {7x-8y=24
\n" ); document.write( " {xy^2=1\r
\n" ); document.write( "\n" ); document.write( "2) {(x+1)^2 - (y-1)^2 = 20
\n" ); document.write( " {x^2 - (y+2)^2 - 24\r
\n" ); document.write( "\n" ); document.write( "Thank you - Lori \n" ); document.write( "
Algebra.Com's Answer #184316 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1) \r\n" );
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document.write( "\"system%287x-8y=24%2C+xy%5E2=1%29\"\r\n" );
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document.write( "solve the first equation for y:\r\n" );
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document.write( "\"7x-8y=24\"\r\n" );
document.write( "\"7x-24=8y\"\r\n" );
document.write( "\"%287x-24%29%2F8=y\"\r\n" );
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document.write( "Substitute in the second equation:\r\n" );
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document.write( "\"x%28%287x-24%29%2F8%29%5E2=1\"\r\n" );
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document.write( "\"x%287x-24%29%5E2%2F64=1\"\r\n" );
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document.write( "Multiply both sides by 64\r\n" );
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document.write( "\"x%287x-24%29%5E2=64\"\r\n" );
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document.write( "Square the binomial:\r\n" );
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document.write( "\"x%2849x%5E2-336x%2B576%29=64\"\r\n" );
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document.write( "\"49x%5E3-336x%5E2%2B576x-64=0\"\r\n" );
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document.write( "Possible rational zeros of that are\r\n" );
document.write( "± fractions whose numerators are\r\n" );
document.write( "factors of 64 and whose denominators \r\n" );
document.write( "are factors of 49.\r\n" );
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document.write( "The factors of 64 are 1,2,4,8,16,32,64\r\n" );
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document.write( "The factors of 49 are 1,7,49\r\n" );
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document.write( "We try the easiest one first in hopes\r\n" );
document.write( "the person who made up this problem\r\n" );
document.write( "was kind.\r\n" );
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document.write( "We try x=1, so we divide by x-1\r\n" );
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document.write( "1 | 49 -336  576 -64 \r\n" );
document.write( "  |      49 -287 289 \r\n" );
document.write( "  ------------------\r\n" );
document.write( "    49 -287  289 225\r\n" );
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document.write( "Doesn't leave a 0 remainder.\r\n" );
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document.write( "We try x=2, so we divide by x-2\r\n" );
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document.write( "2 | 49 -336  576 -64 \r\n" );
document.write( "  |      98 -476 200 \r\n" );
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document.write( "    49 -238  100 136\r\n" );
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document.write( "Doesn't leave a 0 remainder.\r\n" );
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document.write( "We try x=4, so we divide by x-4\r\n" );
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document.write( "4 | 49 -336  576 -64 \r\n" );
document.write( "  |     196 -560  64 \r\n" );
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document.write( "    49 -140   16   0\r\n" );
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document.write( "Hooray! It leaves a 0 remainder!\r\n" );
document.write( "So we have factored the left side of\r\n" );
document.write( "the equation \r\n" );
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document.write( "\"49x%5E3-336x%5E2%2B576x-64=0\"\r\n" );
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document.write( "as\r\n" );
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document.write( "\"%28x-4%29%2849x%5E2-140x%2B16%29=0\"\r\n" );
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document.write( "So we use the zero factor property\r\n" );
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document.write( "\"x-4=0\" which gives the value \"x=4\"\r\n" );
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document.write( "\"49x%5E2-140x%2B16=0\"\r\n" );
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document.write( "That does not factor, so we have to use the quadratic\r\n" );
document.write( "formula:\r\n" );
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document.write( "\"x+=+%28140+%2B-+sqrt%2816464%29%29%2F98+\"\r\n" );
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document.write( "\"x+=+%28140+%2B-+sqrt%28784%2A21%29%29%2F98+\"\r\n" );
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document.write( "\"x+=+%28140+%2B-+28sqrt%2821%29%29%2F98+\"\r\n" );
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document.write( "\"x+=+%2814%2810+%2B-+2sqrt%2821%29%29%29%2F98+\"\r\n" );
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document.write( "\"x+=+%2810+%2B-+2sqrt%2821%29%29%2F7+\"\r\n" );
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document.write( "Now we must substitute each of the 3 values for x\r\n" );
document.write( "into\r\n" );
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document.write( "\"7x-8y=24\"\r\n" );
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document.write( "Substituting \"x=4\"\r\n" );
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document.write( "\"7%284%29-8y=24\"\r\n" );
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document.write( "\"28-8y=24\"\r\n" );
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document.write( "\"4=8y\"\r\n" );
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document.write( "\"4%2F8=y\"\r\n" );
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document.write( "\"1%2F2=y\"\r\n" );
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document.write( "Therefore on soluton is (4,\"1%2F2\")\r\n" );
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document.write( "-----\r\n" );
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document.write( "Substituting \"x+=+%2810+%2B+2sqrt%2821%29%29%2F7+\"\r\n" );
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document.write( "\"7%28+++%2810+%2B+2sqrt%2821%29%29%2F7+++++++++%29-8y=24\"\r\n" );
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document.write( "\"%2810+%2B+2sqrt%2821%29%29-8y=24%7D%7D%0D%0A%0D%0A%7B%7B%7B-14%2B2sqrt%2821%29=8y\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"-7%2Bsqrt%2821%29=4y\"\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "\"%28-7%2Bsqrt%2821%29%29%2F4=y\"\r\n" );
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document.write( "So another solution is \r\n" );
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document.write( "(x,y) = (\"%2810+%2B+2sqrt%2821%29%29%2F7\",\"%28-7%2Bsqrt%2821%29%29%2F4\")\r\n" );
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document.write( "---\r\n" );
document.write( "Substituting \"x+=+%2810+-+2sqrt%2821%29%29%2F7+\"\r\n" );
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document.write( "\"7%28+++%2810+-+2sqrt%2821%29%29%2F7+++++++++%29-8y=24\"\r\n" );
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document.write( "\"%2810+-+2sqrt%2821%29%29-8y=24%7D%7D%0D%0A%0D%0A%7B%7B%7B-14-2sqrt%2821%29=8y\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"-7-sqrt%2821%29=4y\"\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "\"%28-7-sqrt%2821%29%29%2F4=y\"\r\n" );
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document.write( "So another solution is \r\n" );
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document.write( "(x,y) = (\"%2810+-+2sqrt%2821%29%29%2F7\",\"%28-7-sqrt%2821%29%29%2F4\")\r\n" );
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document.write( "---\r\n" );
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document.write( "2)  {(x+1)^2 - (y-1)^2 = 20\r\n" );
document.write( "    {x^2 - (y+2)^2 - 24\r\n" );
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document.write( "Sorry, but you left out the equal sign in the second\r\n" );
document.write( "Re-post it corrected and we can help you.  There must be\r\n" );
document.write( "an equal sign somewhere in that.  You probably meant for \r\n" );
document.write( "one of the - signs to be an = sign but we can't tell \r\n" );
document.write( "which one.\r\n" );
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document.write( "Edwin

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