document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122142>Question 122142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following systems by using either addition or substitution.  if a unique solution does not exist, state whether the system is dependent of inconsistent.\r<BR>\n" );
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document.write( "         10x+2y=7<BR>\n" );
document.write( "             y=-5x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89666 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=89666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B2y=7 ALIGN=MIDDLE  ALT=\"10x%2B2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x%2B3 ALIGN=MIDDLE  ALT=\"y=-5x%2B3\"   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=10x%2B2%28-5x%2B3%29=7 ALIGN=MIDDLE  ALT=\"10x%2B2%28-5x%2B3%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x%2B3 ALIGN=MIDDLE  ALT=\"y=-5x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%2B3 ALIGN=MIDDLE  ALT=\"-5x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-10x%2B6=7 ALIGN=MIDDLE  ALT=\"10x-10x%2B6=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=7 ALIGN=MIDDLE  ALT=\"6=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=7-6 ALIGN=MIDDLE  ALT=\"0=7-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 6 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=1 ALIGN=MIDDLE  ALT=\"0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "Since this equation is <font size=4><b>never</b></font> true for any x value, this means there are no solutions. So the system is inconsistent.<BR>\n" );
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