document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332233>Question 332233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone show me how to use the elimination method to solve this problem.  The solution says it is (4y+1,y) for any real numbers.  I just don't kow how they go it.  Thanks\r<BR>\n" );
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document.write( "2x-8y=2<BR>\n" );
document.write( "3x-12y=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238101 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=238101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It turns out that this system has an infinite number of solutions. Basically one equation is just the other in a different form. So to solve this \"system\", we just need to solve for one variable. So what the book did was solve for 'y' (in either equation). \r<BR>\n" );
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document.write( "So take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-8y=2 ALIGN=MIDDLE  ALT=\"2x-8y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for x to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=8y%2B2 ALIGN=MIDDLE  ALT=\"2x=8y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%288y%2B2%29%2F2 ALIGN=MIDDLE  ALT=\"x=%288y%2B2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4y%2B1 ALIGN=MIDDLE  ALT=\"x=4y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So every 'x' coordinate of the solution is simply equal to 4 times the y coordinate plus one.\r<BR>\n" );
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document.write( "So recall that any solution of a system is of the form (x,y) and we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4y%2B1 ALIGN=MIDDLE  ALT=\"x=4y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the solution is (4y+1,y)\r<BR>\n" );
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document.write( "Note: there are other ways to display the solution, but you essentially get the same thing. </SPAN>\n" );
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