document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4841>Question 4841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by the addition method\r<BR>\n" );
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document.write( "x/3-y/2=-5/6\r<BR>\n" );
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document.write( "x/5-y/3=-3/5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2352 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start by clearing those fractions.  The LCD for the first equation is 6, for the second equation is 15, so multiply both sides of these equations by those numbers respectively:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3-y%2F2=-5%2F6 ALIGN=MIDDLE  ALT=\"x%2F3-y%2F2=-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = First Equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F5-y%2F3=-3%2F5 ALIGN=MIDDLE  ALT=\"x%2F5-y%2F3=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = Second Equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2F3+-+6%2Ay%2F2+=+6%2A%28-5%29%2F6 ALIGN=MIDDLE  ALT=\"6%2Ax%2F3+-+6%2Ay%2F2+=+6%2A%28-5%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+3y+=+-5+ ALIGN=MIDDLE  ALT=\"2x+-+3y+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = First Equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A+x%2F5+-+15%2Ay%2F3+=+15%2A%28-3%29%2F5 ALIGN=MIDDLE  ALT=\"15%2A+x%2F5+-+15%2Ay%2F3+=+15%2A%28-3%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+5y+=+-9 ALIGN=MIDDLE  ALT=\"3x+-+5y+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = Second Equation\r<BR>\n" );
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document.write( "2x - 3y = -5    First Equation<BR>\n" );
document.write( "3x - 5y = -9    Second Equation\r<BR>\n" );
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document.write( "Now, eliminate either the x in these equations by getting a common number of 6 for the x coefficients.  To do this, you must multiply the first equation by 3 and the second equation by -2.  It looks like this:\r<BR>\n" );
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document.write( "3(2x - 3y ) = 3*(-5)<BR>\n" );
document.write( "-2(3x - 5y ) = -2*(-9)\r<BR>\n" );
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document.write( "6x - 9y = -15<BR>\n" );
document.write( "-6x + 10y = 18\r<BR>\n" );
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document.write( "Add the equations together, and you get:<BR>\n" );
document.write( " y = 3\r<BR>\n" );
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document.write( "Substitute y = 3 in the first equation:<BR>\n" );
document.write( "2x - 3y = -5<BR>\n" );
document.write( "2x -3(3) = -5<BR>\n" );
document.write( "2x - 9 = -5    Add +9 to each side of the equation:<BR>\n" );
document.write( "2x - 9 + 9 = -5 + 9<BR>\n" );
document.write( "2x = 4<BR>\n" );
document.write( "x= 2<BR>\n" );
document.write( "  \r<BR>\n" );
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document.write( "Check it by substituting both x and y  in the second equation (NOTE:  To be a valid check, you must substitute into the OTHER equation, not the one you just used!!)<BR>\n" );
document.write( "3x - 5y = -9<BR>\n" );
document.write( "3(2) - 5(3) = -9<BR>\n" );
document.write( "6 - 15 = -9\r<BR>\n" );
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document.write( "Praise the Lord!  It checks!!!\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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