document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115431>Question 115431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> we have been studying systems of nonlinear equations in two variables.<BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "Solve: x^2-y^2=1 and x^2+y=7\r<BR>\n" );
document.write( "\n" );
document.write( "I started by isolating the y variable on the 2nd problem<BR>\n" );
document.write( "                                         y=7-x^2<BR>\n" );
document.write( "Then I know I need to use addition or substitution method to solve:<BR>\n" );
document.write( "I picked substitution method.<BR>\n" );
document.write( "         x^2-(7-x^2)^2=1<BR>\n" );
document.write( "         x^2 -(49-14x^2+x^4)=1<BR>\n" );
document.write( "         x^2-49+14x^2-x^4=1 changed signs because of negative sign.<BR>\n" );
document.write( "         -x^4+15x^2-49=1 combined like terms<BR>\n" );
document.write( "                                 -1  -1<BR>\n" );
document.write( "                               --------<BR>\n" );
document.write( "         -x^4+15x^2-50=0\r<BR>\n" );
document.write( "\n" );
document.write( "          0=x^4-15x^2+50 rewrite for better understanding\r<BR>\n" );
document.write( "\n" );
document.write( "A=x^2  Use this in replacement of x^2\r<BR>\n" );
document.write( "\n" );
document.write( "         0=A^2-15A+50<BR>\n" );
document.write( "        (A-10) (A-5) Factor<BR>\n" );
document.write( "        A=10   A=5\r<BR>\n" );
document.write( "\n" );
document.write( "       Now I place x^2 back in for A<BR>\n" );
document.write( "       x^2=10       x^2=5\r<BR>\n" );
document.write( "\n" );
document.write( "This is where I get lost, I know on old problems I would use my radicand/square root symbol<BR>\n" );
document.write( "over each and x would equal a square root ie: x^2=1     x^2=9<BR>\n" );
document.write( "                                                                                    x= +/-1        x= +/-3\r<BR>\n" );
document.write( "\n" );
document.write( "                        and my answers were:                     (1,3)                (3,1)<BR>\n" );
document.write( "                                                                                     (-1,-3)           (-3,-1)\r<BR>\n" );
document.write( "\n" );
document.write( "Please help me finish this problem:) It's been 2 days trying to figure out what I'm doing wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84022 by </B><A HREF=/tutors/aboutme.mpl?userid=vertciel><B>vertciel(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vertciel><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello there,\r<BR>\n" );
document.write( "\n" );
document.write( "1. x^2 - y^2 = 1 and x^2 + y = 7 \r<BR>\n" );
document.write( "\n" );
document.write( "The easier method is actually elimination. \r<BR>\n" );
document.write( "\n" );
document.write( "If I subtract both equations, I get:\r<BR>\n" );
document.write( "\n" );
document.write( "-y^2 - y = -6\r<BR>\n" );
document.write( "\n" );
document.write( "-y^2 - y + 6 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "-(y^2 + y - 6)= 0\r<BR>\n" );
document.write( "\n" );
document.write( "-(y + 3)(y - 2) = 0\r<BR>\n" );
document.write( "\n" );
document.write( "y = -3, 2\r<BR>\n" );
document.write( "\n" );
document.write( "Can you take it from here?\r<BR>\n" );
document.write( "\n" );
document.write( "2. -x^4 + 15x^2 - 50 = 0 \r<BR>\n" );
document.write( "\n" );
document.write( "Let y = x^2.\r<BR>\n" );
document.write( "\n" );
document.write( "-y^2 + 15y - 50 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "y = 5, 10\r<BR>\n" );
document.write( "\n" );
document.write( "Since y = x^2, you have the following two equations:\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 = 5 and x^2 = 10\r<BR>\n" );
document.write( "\n" );
document.write( "If you square root both sides, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+sqrt%285%29+ ALIGN=MIDDLE  ALT=\"+x+=+sqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+sqrt%2810%29+ ALIGN=MIDDLE  ALT=\"+x+=+sqrt%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you want to check them, plug them into the original equation.\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps! Write back for more help! \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );