document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999141>Question 999141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve using addition method\r<BR>\n" );
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document.write( "3x+7y=16<BR>\n" );
document.write( "2x-3y=-11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616849 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equations are:\r<BR>\n" );
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document.write( "3x+7y=16<BR>\n" );
document.write( "2x-3y=-11\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and multiply both sides of the second equation by 3 to get:\r<BR>\n" );
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document.write( "6x + 14y = 32<BR>\n" );
document.write( "6x - 9y = -33\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "23y = 65\r<BR>\n" );
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document.write( "solve for y to get y = 65/23\r<BR>\n" );
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document.write( "replace y with 65/23 in the original first equation to get:\r<BR>\n" );
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document.write( "3x+7y=16 becomes:<BR>\n" );
document.write( "3x + 7*65/23 = 16\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3x + 455/23 = 16\r<BR>\n" );
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document.write( "multiply both sides of this equation by 23 to get:\r<BR>\n" );
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document.write( "69x + 455 = 368\r<BR>\n" );
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document.write( "subtract 455 from both sides of this equation to get:\r<BR>\n" );
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document.write( "69x = 368 - 455\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "69x = -87\r<BR>\n" );
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document.write( "divide both sides of this equation by 69 to get:\r<BR>\n" );
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document.write( "x = -87/69\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = -87/69<BR>\n" );
document.write( "y = 65/23\r<BR>\n" );
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document.write( "to confirm these solutions are correct, replace x and y in the original equations to get:\r<BR>\n" );
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document.write( "3x+7y=16<BR>\n" );
document.write( "2x-3y=-11\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "3*-87/69 + 7*65/23 = 16<BR>\n" );
document.write( "2*-87/69 - 3*65/23 = -11\r<BR>\n" );
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document.write( "evaluate both equations using your calculator (unless you want to punish yourself by doing the math manually) to get:\r<BR>\n" );
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document.write( "16 = 16<BR>\n" );
document.write( "-11 = -11\r<BR>\n" );
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document.write( "the solutions are confirmed as good.\r<BR>\n" );
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document.write( "x = -87/69<BR>\n" );
document.write( "y = 65/23\r<BR>\n" );
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document.write( "x = -87/69 can be simplified to x = -29/23<BR>\n" );
document.write( "y = 65/23 remains at y = 65/23 since it cannot be simplified any further.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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