document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174563>Question 174563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”<BR>\n" );
document.write( "4x – 3y = 1<BR>\n" );
document.write( "-12x + 9y = 5<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 #129572 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=129572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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%284x-3y=1%2C-12x%2B9y=5%29 ALIGN=MIDDLE  ALT=\"system%284x-3y=1%2C-12x%2B9y=5%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%284x-3y%29=3%281%29 ALIGN=MIDDLE  ALT=\"3%284x-3y%29=3%281%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=12x-9y=3 ALIGN=MIDDLE  ALT=\"12x-9y=3\"   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%2812x-9y=3%2C-12x%2B9y=5%29 ALIGN=MIDDLE  ALT=\"system%2812x-9y=3%2C-12x%2B9y=5%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=%2812x-9y%29%2B%28-12x%2B9y%29=%283%29%2B%285%29 ALIGN=MIDDLE  ALT=\"%2812x-9y%29%2B%28-12x%2B9y%29=%283%29%2B%285%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=%2812x%2B-12x%29%2B%28-9y%2B9y%29=3%2B5 ALIGN=MIDDLE  ALT=\"%2812x%2B-12x%29%2B%28-9y%2B9y%29=3%2B5\"   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=8 ALIGN=MIDDLE  ALT=\"0x%2B0y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=8 ALIGN=MIDDLE  ALT=\"0=8\"   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=8 ALIGN=MIDDLE  ALT=\"0=8\"   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 system is inconsistent.<BR>\n" );
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