document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146532>Question 146532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of Equations\r<BR>\n" );
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document.write( "2/5x + 3/5y = 16/5<BR>\n" );
document.write( "4x + 2y = 40\r<BR>\n" );
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document.write( "I know that some way you have to eliminate the fractions in the first equations. Where I am stuck at is how to eliminate the fractions and what type of method to use to solve it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106963 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=106963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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%282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5%2C4x+%2B+2y+=+40%29 ALIGN=MIDDLE  ALT=\"system%28%282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5%2C4x+%2B+2y+=+40%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=5%28%282%2Fcross%285%29%29x+%2B+%283%2Fcross%285%29%29y+%29=5%28+16%2Fcross%285%29%29 ALIGN=MIDDLE  ALT=\"5%28%282%2Fcross%285%29%29x+%2B+%283%2Fcross%285%29%29y+%29=5%28+16%2Fcross%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by the LCD 5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y=16 ALIGN=MIDDLE  ALT=\"2x%2B3y=16\"   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=-2%282x%2B3y%29=-2%2816%29 ALIGN=MIDDLE  ALT=\"-2%282x%2B3y%29=-2%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now 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-6y=-32 ALIGN=MIDDLE  ALT=\"-4x-6y=-32\"   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%28-4x-6y=-32%2C4x%2B2y=40%29 ALIGN=MIDDLE  ALT=\"system%28-4x-6y=-32%2C4x%2B2y=40%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=%28-4x-6y%29%2B%284x%2B2y%29=%28-32%29%2B%2840%29 ALIGN=MIDDLE  ALT=\"%28-4x-6y%29%2B%284x%2B2y%29=%28-32%29%2B%2840%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%28-6y%2B2y%29=-32%2B40 ALIGN=MIDDLE  ALT=\"%28-4x%2B4x%29%2B%28-6y%2B2y%29=-32%2B40\"   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%2B-4y=8 ALIGN=MIDDLE  ALT=\"0x%2B-4y=8\"   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=-4y=8 ALIGN=MIDDLE  ALT=\"-4y=8\"   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=y=%288%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"y=%288%29%2F%28-4%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( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-6y=-32 ALIGN=MIDDLE  ALT=\"-4x-6y=-32\"   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=-4x-6%28-2%29=-32 ALIGN=MIDDLE  ALT=\"-4x-6%28-2%29=-32\"   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=-4x%2B12=-32 ALIGN=MIDDLE  ALT=\"-4x%2B12=-32\"   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=-4x=-32-12 ALIGN=MIDDLE  ALT=\"-4x=-32-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   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=-4x=-44 ALIGN=MIDDLE  ALT=\"-4x=-44\"   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=x=%28-44%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x=%28-44%29%2F%28-4%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=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=11 ALIGN=MIDDLE  ALT=\"x=11\"   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=11 ALIGN=MIDDLE  ALT=\"x=11\"   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;\" >.\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(11,-2\right)\">.\r<BR>\n" );
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document.write( "This means that the two equations are 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(11,-2\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-3%2C21%2C-12%2C8%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-3%2C21%2C-12%2C8%2C%2816-2x%29%2F%283%29%2C%2840-4x%29%2F%282%29%29%2C%0D%0Acircle%2811%2C-2%2C0.05%29%2C%0D%0Acircle%2811%2C-2%2C0.08%29%2C%0D%0Acircle%2811%2C-2%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=%282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5 ALIGN=MIDDLE  ALT=\"%282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+2y+=+40 ALIGN=MIDDLE  ALT=\"4x+%2B+2y+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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