document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124876>Question 124876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system by substitution \r<BR>\n" );
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document.write( "4x-12y=5, <BR>\n" );
document.write( "-x+3y= -1\r<BR>\n" );
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document.write( "Show your solution below:\r<BR>\n" );
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document.write( "What is the solution for this system? \r<BR>\n" );
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document.write( "What type of system is this? <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 #91526 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=91526\">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%284x-12y=5%2C-x%2B3y=-1%29 ALIGN=MIDDLE  ALT=\"system%284x-12y=5%2C-x%2B3y=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-12y=5 ALIGN=MIDDLE  ALT=\"4x-12y=5\"   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=-12y=5-4x ALIGN=MIDDLE  ALT=\"-12y=5-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   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=-12y=-4x%2B5 ALIGN=MIDDLE  ALT=\"-12y=-4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4x%2B5%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"y=%28-4x%2B5%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   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=%28%28-4%29%2F%28-12%29%29x%2B%285%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"y=%28%28-4%29%2F%28-12%29%29x%2B%285%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x-5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x-5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now 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;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"%281%2F3%29x-5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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%2B3highlight%28%28%281%2F3%29x-5%2F12%29%29=-1 ALIGN=MIDDLE  ALT=\"-x%2B3highlight%28%28%281%2F3%29x-5%2F12%29%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x-5%2F12\"   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=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"%281%2F3%29x-5%2F12\"   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=-x%2B%283%29%281%2F3%29x%2B%283%29%28-5%2F12%29=-1 ALIGN=MIDDLE  ALT=\"-x%2B%283%29%281%2F3%29x%2B%283%29%28-5%2F12%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x-5%2F12 ALIGN=MIDDLE  ALT=\"%281%2F3%29x-5%2F12\"   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%2B%283%2F3%29x-15%2F12=-1 ALIGN=MIDDLE  ALT=\"-x%2B%283%2F3%29x-15%2F12=-1\"   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=%2812%29%28-1x%2B%283%2F3%29x-15%2F12%29=%2812%29%28-1%29 ALIGN=MIDDLE  ALT=\"%2812%29%28-1x%2B%283%2F3%29x-15%2F12%29=%2812%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 12. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12x%2B12x-15=-12 ALIGN=MIDDLE  ALT=\"-12x%2B12x-15=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply the LCM to each side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15=-12 ALIGN=MIDDLE  ALT=\"-15=-12\"   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=-12%2B15 ALIGN=MIDDLE  ALT=\"0=-12%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 15 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3 ALIGN=MIDDLE  ALT=\"0=3\"   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.\r<BR>\n" );
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