document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=324946>Question 324946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2y + 3x = 12<BR>\n" );
document.write( "-4y + 5x = -2\r<BR>\n" );
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document.write( "How do I solve the above linear equations using the elimination method? I don't understand  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232675 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=232675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by eliminiation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B3x+=+12 ALIGN=MIDDLE  ALT=\"2y%2B3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B5x+=+-2 ALIGN=MIDDLE  ALT=\"-4y%2B5x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here you have two equations in two unknowns.  The idea behind the \"elimination\" method is to eliminate one of the variables (either x or y) then solve for the remaining variable.  Once you know the value of one of the variables, you can find the value of the other one by substitution.<BR>\n" );
document.write( "Let's start:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B3x+=+12 ALIGN=MIDDLE  ALT=\"2y%2B3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply this equation by 2.<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B5x+=+-2 ALIGN=MIDDLE  ALT=\"-4y%2B5x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------- <BR>\n" );
document.write( "1a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B6x+=+24 ALIGN=MIDDLE  ALT=\"4y%2B6x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B5x+=+-2 ALIGN=MIDDLE  ALT=\"-4y%2B5x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add these two equations to eliminate the y-variable.<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x+=+22 ALIGN=MIDDLE  ALT=\"11x+=+22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 11.<BR>\n" );
document.write( "3a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitute this value of x into either one of the two original equations to solve for y. Let's use equation 1).<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B3x+=+12 ALIGN=MIDDLE  ALT=\"2y%2B3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 2.<BR>\n" );
document.write( "1a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B3%282%29+=+12 ALIGN=MIDDLE  ALT=\"2y%2B3%282%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B6+=+12 ALIGN=MIDDLE  ALT=\"2y%2B6+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6 from both sides.<BR>\n" );
document.write( "1c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+6 ALIGN=MIDDLE  ALT=\"2y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.<BR>\n" );
document.write( "1d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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