document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168732>Question 168732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve  each  system by  any method\r<BR>\n" );
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document.write( "1 x-3y=1<BR>\n" );
document.write( "  3x-5y=-5\r<BR>\n" );
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document.write( "2 2x-3y=5<BR>\n" );
document.write( "  4x-6y=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124373 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=124373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "Substitution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3y=1 ALIGN=MIDDLE  ALT=\"x-3y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y%2B1 ALIGN=MIDDLE  ALT=\"x=3y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3y to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5y=-5 ALIGN=MIDDLE  ALT=\"3x-5y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%283y%2B1%29-5y=-5 ALIGN=MIDDLE  ALT=\"3%283y%2B1%29-5y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y%2B1 ALIGN=MIDDLE  ALT=\"x=3y%2B1\"   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=9y%2B3-5y=-5 ALIGN=MIDDLE  ALT=\"9y%2B3-5y=-5\"   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=4y%2B3=-5 ALIGN=MIDDLE  ALT=\"4y%2B3=-5\"   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=4y=-5-3 ALIGN=MIDDLE  ALT=\"4y=-5-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-8 ALIGN=MIDDLE  ALT=\"4y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-8%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y=%28-8%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y%2B1 ALIGN=MIDDLE  ALT=\"x=3y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the first isolated equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%28-2%29%2B1 ALIGN=MIDDLE  ALT=\"x=3%28-2%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   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=x=-6%2B1 ALIGN=MIDDLE  ALT=\"x=-6%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which form the ordered pair (-5, -2)\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Elimination:\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-3y=5%2C4x-6y=3%29 ALIGN=MIDDLE  ALT=\"system%282x-3y=5%2C4x-6y=3%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%282x-3y%29=-2%285%29 ALIGN=MIDDLE  ALT=\"-2%282x-3y%29=-2%285%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=-4x%2B6y=-10 ALIGN=MIDDLE  ALT=\"-4x%2B6y=-10\"   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( "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=%28-4x%2B6y%29%2B%284x-6y%29=%28-10%29%2B%283%29 ALIGN=MIDDLE  ALT=\"%28-4x%2B6y%29%2B%284x-6y%29=%28-10%29%2B%283%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=%28-4x%2B4x%29%2B%286y%2B-6y%29=-10%2B3 ALIGN=MIDDLE  ALT=\"%28-4x%2B4x%29%2B%286y%2B-6y%29=-10%2B3\"   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=-7 ALIGN=MIDDLE  ALT=\"0x%2B0y=-7\"   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=-7 ALIGN=MIDDLE  ALT=\"0=-7\"   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=-7 ALIGN=MIDDLE  ALT=\"0=-7\"   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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