document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243674>Question 243674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> without graphing, solve each equation and determine whether each system has no solution, one solution or an infinite number of solutions<BR>\n" );
document.write( "5x-8y=24<BR>\n" );
document.write( "10x-16y= -9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178485 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=178485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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%285x-8y=24%2C10x-16y=-9%29 ALIGN=MIDDLE  ALT=\"system%285x-8y=24%2C10x-16y=-9%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=-2%285x-8y%29=-2%2824%29 ALIGN=MIDDLE  ALT=\"-2%285x-8y%29=-2%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x%2B16y=-48 ALIGN=MIDDLE  ALT=\"-10x%2B16y=-48\"   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%28-10x%2B16y=-48%2C10x-16y=-9%29 ALIGN=MIDDLE  ALT=\"system%28-10x%2B16y=-48%2C10x-16y=-9%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=%28-10x%2B16y%29%2B%2810x-16y%29=%28-48%29%2B%28-9%29 ALIGN=MIDDLE  ALT=\"%28-10x%2B16y%29%2B%2810x-16y%29=%28-48%29%2B%28-9%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=%28-10x%2B10x%29%2B%2816y%2B-16y%29=-48%2B-9 ALIGN=MIDDLE  ALT=\"%28-10x%2B10x%29%2B%2816y%2B-16y%29=-48%2B-9\"   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=-57 ALIGN=MIDDLE  ALT=\"0x%2B0y=-57\"   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=-57 ALIGN=MIDDLE  ALT=\"0=-57\"   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=-57 ALIGN=MIDDLE  ALT=\"0=-57\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>never</b></font> true, this means that there are no solutions. \r<BR>\n" );
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document.write( "So the system is inconsistent.<BR>\n" );
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