document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190343>Question 1190343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am really having a hard time understanding solving using substitution \r<BR>\n" );
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document.write( "2x+3y=24<BR>\n" );
document.write( "-3x-5y=15\r<BR>\n" );
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document.write( "how do I solve those using substitution  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821959 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "(1) I personally would never solve a pair of equations like this using substitution.  When the equations are both in this form (\"Ax+By=C\"), I would always use elimination.<br><BR>\n" );
document.write( "2x+3y=24<BR>\n" );
document.write( "-3x-5y=15<br><BR>\n" );
document.write( "multiply the first equation by 3 and the second by 2 so that the x terms are 6x and -6x; then adding the two equations eliminates x.  You can then solve for y, and once you have y you can use either original equation to solve for x.<br><BR>\n" );
document.write( "6x+9y=72<BR>\n" );
document.write( "-6x-10y=30<BR>\n" );
document.write( "-y=102<BR>\n" );
document.write( "y=-102<br><BR>\n" );
document.write( "2x+3(-102)=24<BR>\n" );
document.write( "2x-306=24<BR>\n" );
document.write( "2x=330<BR>\n" );
document.write( "x=165<br><BR>\n" );
document.write( "ANSWER: x=165; y=-102<br><BR>\n" );
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document.write( "(2) Solving by substitution, you solve one equation for one variable in terms of the other and substitute that into the other equation.<br><BR>\n" );
document.write( "solve the first equation for x:<BR>\n" );
document.write( "2x+3y=24<BR>\n" );
document.write( "2x=-3y+24<BR>\n" );
document.write( "x=-1.5y+12<br><BR>\n" );
document.write( "substitute that expression for x in the second equation:<BR>\n" );
document.write( "-3(-1.5)y+12)-5y=15<BR>\n" );
document.write( "4.5y-36-5y=15<BR>\n" );
document.write( "-.5y=51<BR>\n" );
document.write( "y=51/-.5=-102<br><BR>\n" );
document.write( "x=(-1.5)(-102)+12=153+12=165<br><BR>\n" );
document.write( "Same answer; but the work is a lot uglier....<br><BR>\n" );
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