document.write( "Question 1062395: I am trying to figure how to find part of answer to this non-linear system:
\n" ); document.write( "(X+1)^2 - (y-1)^2 = 20
\n" ); document.write( "X^2 - (y+2)^2 = 24\r
\n" ); document.write( "\n" ); document.write( "I used elimination to end up with the answers of y = 1/2 and x = -11/2. \r
\n" ); document.write( "\n" ); document.write( "This has been confirmed via graphing. Problem is there is another common point of 5,-3, but I cannot figure out how to come do it algebraically. Any help would be appreciated. Thank you! \n" ); document.write( "

Algebra.Com's Answer #677296 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "(x+1)^2 - (y-1)^2 = 20
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document.write( "(x+1)^2 - (y-1)^2 = 20,    (1)\r\n" );
document.write( "X^2 - (y+2)^2     = 24.    (2)\r\n" );
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document.write( "Open parentheses:\r\n" );
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document.write( "x^2 + 2x + 1 - y^2 + 2y - 1 = 20,    (3)     \r\n" );
document.write( "x^2          - y^2 - 4y - 4 = 24.    (4)\r\n" );
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document.write( "Distract (4) from (3) (both sides). You will get\r\n" );
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document.write( "2x + 1 + 6y + 3 = -4,   or\r\n" );
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document.write( "2x + 6y = -8,   or\r\n" );
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document.write( "x + 3y = -4.                          (5)\r\n" );
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document.write( "Express x = -3y - 4 from (5) and substitute it into (2), replacing x. You will get\r\n" );
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document.write( "(-3y - 4)^2 - (y+2)^2 = 24,   or\r\n" );
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document.write( "9y^2 + 24y + 16 - y^2 - 4y - 4 = 24,   or\r\n" );
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document.write( "8y^2 + 20y - 12 = 0,   or\r\n" );
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document.write( "2y^2 + 5y - 3 = 0.\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "The roots are  = ,   = -3.\r\n" );
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document.write( "For each root  find the corresponding value of x.\r\n" );
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document.write( "Can you complete it on your own?\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see more similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving systems of algebraic equations of degree 2 \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Systems of equations that are not linear\".\r
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