document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283289>Question 283289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve: x+y=12<BR>\n" );
document.write( "              3x-2y=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205651 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=205651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have two equations and two unknowns, so treat them as a system of linear equations:<BR>\n" );
document.write( "x+y=12<BR>\n" );
document.write( "3x-2y=6<BR>\n" );
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document.write( "multiply the first equation by 2 and add the two equations together<BR>\n" );
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document.write( "2x +2y = 24<BR>\n" );
document.write( "3x -2y = 6<BR>\n" );
document.write( "5x = 30<BR>\n" );
document.write( "x = 6<BR>\n" );
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document.write( "x+y=12<BR>\n" );
document.write( "y = 12-x = 12-6 = 6<BR>\n" );
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document.write( "Check by substituting in the second equation.<BR>\n" );
document.write( "3x = 3(6) = 18<BR>\n" );
document.write( "-2y = -2(6) = -12<BR>\n" );
document.write( "18-12 = 6<BR>\n" );
document.write( "Correct<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "y = 6<BR>\n" );
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document.write( "You also can check graphically to see if they two lines cross at (6,6)...<BR>\n" );
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document.write( "Get the equations into slope-intercept form and define the lines.<BR>\n" );
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document.write( "x+y=12<BR>\n" );
document.write( "y = -x+12<BR>\n" );
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document.write( "3x-2y=6<BR>\n" );
document.write( "-2y = -3x +6<BR>\n" );
document.write( "y = 3/2x -3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-x%2B12%2C3%2F2%2Ax-3%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-x%2B12%2C3%2F2%2Ax-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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