document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469016>Question 469016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by substitution:<BR>\n" );
document.write( "-3x+6y=21<BR>\n" );
document.write( "2x-4y=14\r<BR>\n" );
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document.write( "I have tryed completing this by making the -3x+6y=21 into an x=2y-7.<BR>\n" );
document.write( "Then I got 2(2y-7)-4y=14 which turns into 4y-14-4y=14 and then -14=14.\r<BR>\n" );
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document.write( "If this problem is not possible, then what do I write as an answer??\r<BR>\n" );
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document.write( "Thank you so so so so so so much! (: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321786 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=321786\">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%28-3x%2B6y=21%2C2x-4y=14%29 ALIGN=MIDDLE  ALT=\"system%28-3x%2B6y=21%2C2x-4y=14%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=-3x%2B6y=21 ALIGN=MIDDLE  ALT=\"-3x%2B6y=21\"   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=6y=21%2B3x ALIGN=MIDDLE  ALT=\"6y=21%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=%2B3x%2B21 ALIGN=MIDDLE  ALT=\"6y=%2B3x%2B21\"   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%2B3x%2B21%29%2F%286%29 ALIGN=MIDDLE  ALT=\"y=%28%2B3x%2B21%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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%2B3%29%2F%286%29%29x%2B%2821%29%2F%286%29 ALIGN=MIDDLE  ALT=\"y=%28%28%2B3%29%2F%286%29%29x%2B%2821%29%2F%286%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%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B7%2F2\"   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%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B7%2F2\"   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%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x%2B7%2F2\"   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=2x-4highlight%28%28%281%2F2%29x%2B7%2F2%29%29=14 ALIGN=MIDDLE  ALT=\"2x-4highlight%28%28%281%2F2%29x%2B7%2F2%29%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the second 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%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x%2B7%2F2\"   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=2x%2B%28-4%29%281%2F2%29x%2B%28-4%29%287%2F2%29=14 ALIGN=MIDDLE  ALT=\"2x%2B%28-4%29%281%2F2%29x%2B%28-4%29%287%2F2%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x%2B7%2F2\"   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=2x-%284%2F2%29x-28%2F2=14 ALIGN=MIDDLE  ALT=\"2x-%284%2F2%29x-28%2F2=14\"   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=%282%29%282x-%284%2F2%29x-28%2F2%29=%282%29%2814%29 ALIGN=MIDDLE  ALT=\"%282%29%282x-%284%2F2%29x-28%2F2%29=%282%29%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 2. 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=4x-4x-28=28 ALIGN=MIDDLE  ALT=\"4x-4x-28=28\"   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=-28=28 ALIGN=MIDDLE  ALT=\"-28=28\"   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=28%2B28 ALIGN=MIDDLE  ALT=\"0=28%2B28\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 28 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=56 ALIGN=MIDDLE  ALT=\"0=56\"   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.\r<BR>\n" );
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document.write( "So consequently, there are no solutions for the system of equations.\r<BR>\n" );
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document.write( "So the system is inconsistent.<BR>\n" );
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