document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148123>Question 148123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to solve the following system of linear equation. \r<BR>\n" );
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document.write( "x/4 - y/11 = -9/44\r<BR>\n" );
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document.write( "x/6 - y/13 = -1/26\r<BR>\n" );
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document.write( "Now i am familiar with the methods of solving these types of problems, such as addition method and substitution method, but when it comes to fractions, I'm lost. \r<BR>\n" );
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document.write( "When you solve, would it be possible to explain each step. \r<BR>\n" );
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document.write( "Thanks for all your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108520 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=108520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4-y%2F11=-9%2F44 ALIGN=MIDDLE  ALT=\"x%2F4-y%2F11=-9%2F44\"   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=44%28x%2Fcross%284%29-y%2Fcross%2811%29%29=44%28-9%2Fcross%2844%29%29 ALIGN=MIDDLE  ALT=\"44%28x%2Fcross%284%29-y%2Fcross%2811%29%29=44%28-9%2Fcross%2844%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x-4y=-9 ALIGN=MIDDLE  ALT=\"11x-4y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6-y%2F13=-1%2F26 ALIGN=MIDDLE  ALT=\"x%2F6-y%2F13=-1%2F26\"   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=78%28x%2Fcross%286%29-y%2Fcross%2813%29%29=78%28-1%2Fcross%2826%29%29 ALIGN=MIDDLE  ALT=\"78%28x%2Fcross%286%29-y%2Fcross%2813%29%29=78%28-1%2Fcross%2826%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78 ALIGN=MIDDLE  ALT=\"78\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x-6y=-3 ALIGN=MIDDLE  ALT=\"13x-6y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So now we have the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2811x-4y=-9%2C13x-6y=-3%29 ALIGN=MIDDLE  ALT=\"system%2811x-4y=-9%2C13x-6y=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve this system by use of elimination.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2811x-4y%29=6%28-9%29 ALIGN=MIDDLE  ALT=\"6%2811x-4y%29=6%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 6.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66x-24y=-54 ALIGN=MIDDLE  ALT=\"66x-24y=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2813x-6y%29=-4%28-3%29 ALIGN=MIDDLE  ALT=\"-4%2813x-6y%29=-4%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the second equation by -4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-52x%2B24y=12 ALIGN=MIDDLE  ALT=\"-52x%2B24y=12\"   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%2866x-24y=-54%2C-52x%2B24y=12%29 ALIGN=MIDDLE  ALT=\"system%2866x-24y=-54%2C-52x%2B24y=12%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=%2866x-24y%29%2B%28-52x%2B24y%29=%28-54%29%2B%2812%29 ALIGN=MIDDLE  ALT=\"%2866x-24y%29%2B%28-52x%2B24y%29=%28-54%29%2B%2812%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=%2866x%2B-52x%29%2B%28-24y%2B24y%29=-54%2B12 ALIGN=MIDDLE  ALT=\"%2866x%2B-52x%29%2B%28-24y%2B24y%29=-54%2B12\"   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=14x%2B0y=-42 ALIGN=MIDDLE  ALT=\"14x%2B0y=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the y terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x=-42 ALIGN=MIDDLE  ALT=\"14x=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-42%29%2F%2814%29 ALIGN=MIDDLE  ALT=\"x=%28-42%29%2F%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66x-24y=-54 ALIGN=MIDDLE  ALT=\"66x-24y=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%28-3%29-24y=-54 ALIGN=MIDDLE  ALT=\"66%28-3%29-24y=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   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=-198-24y=-54 ALIGN=MIDDLE  ALT=\"-198-24y=-54\"   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=-24y=-54%2B198 ALIGN=MIDDLE  ALT=\"-24y=-54%2B198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198 ALIGN=MIDDLE  ALT=\"198\"   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=-24y=144 ALIGN=MIDDLE  ALT=\"-24y=144\"   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=%28144%29%2F%28-24%29 ALIGN=MIDDLE  ALT=\"y=%28144%29%2F%28-24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24 ALIGN=MIDDLE  ALT=\"-24\"   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=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Which form the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-3,-6\right)\">.\r<BR>\n" );
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document.write( "This means that the system is consistent and independent.\r<BR>\n" );
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document.write( "Notice when we graph the equations, we see that they intersect at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-3,-6\right)\">. So this visually verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-13%2C7%2C-16%2C4%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-13%2C7%2C-16%2C4%2C%28-9-11x%29%2F%28-4%29%2C%28-3-13x%29%2F%28-6%29%29%2C%0D%0Acircle%28-3%2C-6%2C0.05%29%2C%0D%0Acircle%28-3%2C-6%2C0.08%29%2C%0D%0Acircle%28-3%2C-6%2C0.10%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x-4y=-9 ALIGN=MIDDLE  ALT=\"11x-4y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x-6y=-3 ALIGN=MIDDLE  ALT=\"13x-6y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) <BR>\n" );
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