document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182549>Question 182549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3b.<BR>\n" );
document.write( "this one has me simply dumbfounded. Please help if you can. Thanks.\r<BR>\n" );
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document.write( "How many solutions does the following system have:<BR>\n" );
document.write( "4x + 8y = 16<BR>\n" );
document.write( "3x + 6y = 9<BR>\n" );
document.write( "Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting expression.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137025 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=137025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many solutions does the following system have:<BR>\n" );
document.write( "4x + 8y = 16<BR>\n" );
document.write( "3x + 6y = 9<BR>\n" );
document.write( "Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting expression. <BR>\n" );
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document.write( "Put each equation in slope-intercept form:<BR>\n" );
document.write( "y = (-1/2)x + 2<BR>\n" );
document.write( "y = (-1/2)x + (3/2)<BR>\n" );
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document.write( "They have the same slope and different y-intercepts so there are zero solutions.<BR>\n" );
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document.write( "By elimination:<BR>\n" );
document.write( "4x + 8y = 16<BR>\n" );
document.write( "3x + 6y = 9<BR>\n" );
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document.write( "Multiply thru the 2nd Eq. by (4/3) to get:<BR>\n" );
document.write( "4x + 8y = 16<BR>\n" );
document.write( "4x + 8y = 12<BR>\n" );
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document.write( "Subtracting 2nd by 1st you get:<BR>\n" );
document.write( "0 = 4<BR>\n" );
document.write( "The system is inconsistent and has no solutions.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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