document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147216>Question 147216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When solving a system of equations, how do I know what numbers to put in place of x and y? An example is:\r<BR>\n" );
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document.write( "2x – 6y = 42<BR>\n" );
document.write( "3x – 9y = -15\r<BR>\n" );
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document.write( "I am to solve similar systems of equations but I do not understand what nubers to replace the variables with.\r<BR>\n" );
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document.write( "Can you help?\r<BR>\n" );
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document.write( "Thank you very much.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107577 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=107577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-6y=42%2C3x-9y=-15%29 ALIGN=MIDDLE  ALT=\"system%282x-6y=42%2C3x-9y=-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%282x-6y%29=-3%2842%29 ALIGN=MIDDLE  ALT=\"-3%282x-6y%29=-3%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B18y=-126 ALIGN=MIDDLE  ALT=\"-6x%2B18y=-126\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283x-9y%29=2%28-15%29 ALIGN=MIDDLE  ALT=\"2%283x-9y%29=2%28-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the second equation by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-18y=-30 ALIGN=MIDDLE  ALT=\"6x-18y=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-6x%2B18y=-126%2C6x-18y=-30%29 ALIGN=MIDDLE  ALT=\"system%28-6x%2B18y=-126%2C6x-18y=-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6x%2B18y%29%2B%286x-18y%29=%28-126%29%2B%28-30%29 ALIGN=MIDDLE  ALT=\"%28-6x%2B18y%29%2B%286x-18y%29=%28-126%29%2B%28-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6x%2B6x%29%2B%2818y%2B-18y%29=-126%2B-30 ALIGN=MIDDLE  ALT=\"%28-6x%2B6x%29%2B%2818y%2B-18y%29=-126%2B-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y=-156 ALIGN=MIDDLE  ALT=\"0x%2B0y=-156\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the x terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-156 ALIGN=MIDDLE  ALT=\"0=-156\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-156 ALIGN=MIDDLE  ALT=\"0=-156\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>never</b></font> true, this means that there are no solutions. So the two equations are inconsistent.<BR>\n" );
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