document.write( "Question 983071: Solve the system of equations\r
\n" ); document.write( "\n" ); document.write( "x^2 + y^2 - x - y = 18
\n" ); document.write( "xy + 2x + 2y = 26\r
\n" ); document.write( "\n" ); document.write( "I'm really having hard time at this part. \n" ); document.write( "

Algebra.Com's Answer #603917 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Instead of doing your problem for you, I will do one exactly \r\n" );
document.write( "in every detail step-by-step like your problem.  All you have\r\n" );
document.write( "to do is use the problem below as a model. The problem I will\r\n" );
document.write( "do is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "One thing we observe about this problem is that it is symmetrical\r\n" );
document.write( "in x and y.  That is we have the same two equations if we interchange\r\n" );
document.write( "x and y.  Therefore any time we get a pair of solutions for x, one will\r\n" );
document.write( "be a solution for x and the other will be a solution for y.\r\n" );
document.write( "\r\n" );
document.write( "Solve the second for y\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Substitute in the first equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by (x+2)², [but we know x can't be -2]\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get binomials in descending order:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Looking at the graph on a graphing calculator it appears that \r\n" );
document.write( "it has solutions 2 and 5 but it probably has a pair of conjugate\r\n" );
document.write( "complex solutions too.  We use synthetic division with x=2\r\n" );
document.write( "\r\n" );
document.write( "2 | 1 1 -6 -200  400\r\n" );
document.write( "  |   2  6    0 -400 \r\n" );
document.write( "    1 3  0 -200    0\r\n" );
document.write( "\r\n" );
document.write( "5 | 1  3   0 -200\r\n" );
document.write( "  |    5  40  200    \r\n" );
document.write( "    1  8  40    0\r\n" );
document.write( "\r\n" );
document.write( "So we have factored the polynomial as\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have solutions x=2, x=5, \r\n" );
document.write( "\r\n" );
document.write( "By the symmetry, we know that when x=2, y=5\r\n" );
document.write( "and when x=5, y=2.\r\n" );
document.write( "\r\n" );
document.write( "we get the other solutions from\r\n" );
document.write( "using the quadratic formula, since it won't factor.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the other pair of solutions, by symmetry, are\r\n" );
document.write( "\r\n" );
document.write( "if , then \r\n" );
document.write( "\r\n" );
document.write( "and \r\n" );
document.write( "\r\n" );
document.write( "if , then \r\n" );
document.write( "\r\n" );
document.write( "Now you do your problem exactly step-by step like I did this one.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );