document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121467>Question 121467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me pick the correct answer.\r<BR>\n" );
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document.write( "If x-y=6 and 3x^2+3xy-6y^2=60, then 9x+18y=\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "a) 12<BR>\n" );
document.write( "b) 15<BR>\n" );
document.write( "c) 20<BR>\n" );
document.write( "d) 24<BR>\n" );
document.write( "e) 30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89158 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=89158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If x-y=6 and 3x^2+3xy-6y^2=60, then 9x+18y=\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "a) 12<BR>\n" );
document.write( "b) 15<BR>\n" );
document.write( "c) 20<BR>\n" );
document.write( "d) 24<BR>\n" );
document.write( "e) 30<br>\r<BR>\n" );
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document.write( "I am sure there is an easier way to do this but I can't think of one so I did it the long way.  First we need to set up a system of two equations and then solve it.  The system is:<br>\r<BR>\n" );
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document.write( "x-y = 6<BR>\n" );
document.write( "3x^2+3xy-6y^2 = 60<br>\r<BR>\n" );
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document.write( "so now to solve that mess.  I would start by solving the first equation for x.<br>\r<BR>\n" );
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document.write( "x = 6+y<br>\r<BR>\n" );
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document.write( "Now plug that into the second equation and solve for your y value.<br>\r<BR>\n" );
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document.write( "3(6+y)^2+ 3(6+y)y-6y^2 = 60<BR>\n" );
document.write( "3(6+y)(6+y) + 3y(6+y)-6y^2 = 60 <---- just rearranging some stuff here<BR>\n" );
document.write( "3(36+12y+y^2) + 18y + 3y^2 - 6y^2 = 60 <--- F.O.I.L. and distribute<BR>\n" );
document.write( "108 + 36y + 3y^2 + 18y + 3y^2 - 6y^2 = 60 <--- Multiplying<BR>\n" );
document.write( "3y^2 + 3y^2 - 6y^2 + 36y + 18y + 108 =60 <--- rearranging<BR>\n" );
document.write( "54y + 108 = 60 <--- combining like terms<BR>\n" );
document.write( "54y = -48 <--- starting to solve for y, subtracting 108 from both sides<BR>\n" );
document.write( "y = -48/54 <--- solving for y, dividing both sides by 54<BR>\n" );
document.write( "y = -8/9 <--- simplifying the fraction<br>\r<BR>\n" );
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document.write( "now that we have y = -8/9 we can solve for x.<br>\r<BR>\n" );
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document.write( "x = 6 + y<BR>\n" );
document.write( "x = 6 - 8/9<BR>\n" );
document.write( "x = 46/9<br>\r<BR>\n" );
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document.write( "now we can just plug in those values into 9x+18y and see what it equals.<br>\r<BR>\n" );
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document.write( "9x+18y<BR>\n" );
document.write( "= 9(46/9) + 18(-8/9)<BR>\n" );
document.write( "= 46 - 16<BR>\n" );
document.write( "= 30 or answer e </SPAN>\n" );
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