document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430710>Question 430710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If anyone could please help me to solve these four problems it would be awesome! I am extremely lost. Please help! Thanks!! They use the Substituion Method & Addition Method. I can't figure out the solution sets. Thank you!\r<BR>\n" );
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document.write( "#1 Substituion Method:<BR>\n" );
document.write( "x+y=1<BR>\n" );
document.write( "x^2+xy-y^2=-11\r<BR>\n" );
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document.write( "#2 Substituion Method:<BR>\n" );
document.write( "x^2+y^2=180<BR>\n" );
document.write( "x-y=-6\r<BR>\n" );
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document.write( "#3 Addition Method:<BR>\n" );
document.write( "2x^2+3y^2-30=0<BR>\n" );
document.write( "5x^2-7y^2-17=0\r<BR>\n" );
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document.write( "#4 Addition Method:<BR>\n" );
document.write( "x^2+y^2=16<BR>\n" );
document.write( "y^2-3x=16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299070 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=299070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1 Substituion Method:<BR>\n" );
document.write( "x+y=1<BR>\n" );
document.write( "x^2+xy-y^2=-11<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 1-x<BR>\n" );
document.write( "Substitute:<BR>\n" );
document.write( "x^2+x(1-x)-(1-x)^2 = -11<BR>\n" );
document.write( "----<BR>\n" );
document.write( "x^2+x-x^2-(1-2x+x^2) = -11<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x-1+2x-x^2 = -11<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2-3x-10 = 0<BR>\n" );
document.write( "(x-5)(x+2) = 0<BR>\n" );
document.write( "x = 5 or x = -2<BR>\n" );
document.write( "If x = 5, y = -4<BR>\n" );
document.write( "If x = -2, y = 3<BR>\n" );
document.write( "==========================<BR>\n" );
document.write( " <BR>\n" );
document.write( "#2 Substituion Method:<BR>\n" );
document.write( "x^2+y^2=180<BR>\n" );
document.write( "x-y=-6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = y-6<BR>\n" );
document.write( "Substitute:<BR>\n" );
document.write( "(y-6)^2+y^2 = 180<BR>\n" );
document.write( "y^2-12y+36+y^2 = 180<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2y^2-12y-144 = 0<BR>\n" );
document.write( "y^2-6y-72 = 0<BR>\n" );
document.write( "(y-12)(y+6) = 0<BR>\n" );
document.write( "y = 12 or y = -6<BR>\n" );
document.write( "----<BR>\n" );
document.write( "If y = 12, x = 6<BR>\n" );
document.write( "If y = -6, y -12<BR>\n" );
document.write( "========================= \r<BR>\n" );
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document.write( "#3 Addition Method:<BR>\n" );
document.write( "2x^2+3y^2-30=0<BR>\n" );
document.write( "5x^2-7y^2-17=0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Multiply thru the top equation by 5<BR>\n" );
document.write( "Multiply thru the bottom equation by 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Subtract, then solve for \"y\".<BR>\n" );
document.write( "Then solve for \"x\".<BR>\n" );
document.write( "-------------------------\r<BR>\n" );
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document.write( "#4 Addition Method:<BR>\n" );
document.write( "x^2+y^2=16<BR>\n" );
document.write( "y^2-3x=16<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Subtract to get:<BR>\n" );
document.write( "x^2+3x=0<BR>\n" );
document.write( "x(x+3) = 0<BR>\n" );
document.write( "x = 0 or x = -3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If x = 0, y = 4 or -4<BR>\n" );
document.write( "If x = -3, y = sqrt(7) or -sqrt(7)<BR>\n" );
document.write( "=========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );