document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185456>Question 185456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Think i did them right but 2 & 3 are I get no solution and want to make sure I am not leaving something out.\r<BR>\n" );
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document.write( "1.	Solve by substitution or elimination method: \r<BR>\n" );
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document.write( "              3x – 2y = 26<BR>\n" );
document.write( "             -7x + 3y = -49\r<BR>\n" );
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document.write( "2.	Solve by substitution or elimination method: \r<BR>\n" );
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document.write( "           4x – 5y = 14<BR>\n" );
document.write( "             -12x + 15y = -42\r<BR>\n" );
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document.write( "3.	Solve by substitution or elimination method: \r<BR>\n" );
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document.write( "                 -2x + 6y = 19<BR>\n" );
document.write( "              10x – 30y = -15<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139129 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=139129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "Let's solve this system by 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%283x-2y=26%2C-7x%2B3y=-49%29 ALIGN=MIDDLE  ALT=\"system%283x-2y=26%2C-7x%2B3y=-49%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=3%283x-2y%29=3%2826%29 ALIGN=MIDDLE  ALT=\"3%283x-2y%29=3%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-6y=78 ALIGN=MIDDLE  ALT=\"9x-6y=78\"   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%28-7x%2B3y%29=2%28-49%29 ALIGN=MIDDLE  ALT=\"2%28-7x%2B3y%29=2%28-49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the second equation by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x%2B6y=-98 ALIGN=MIDDLE  ALT=\"-14x%2B6y=-98\"   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%289x-6y=78%2C-14x%2B6y=-98%29 ALIGN=MIDDLE  ALT=\"system%289x-6y=78%2C-14x%2B6y=-98%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=%289x-6y%29%2B%28-14x%2B6y%29=%2878%29%2B%28-98%29 ALIGN=MIDDLE  ALT=\"%289x-6y%29%2B%28-14x%2B6y%29=%2878%29%2B%28-98%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=%289x%2B-14x%29%2B%28-6y%2B6y%29=78%2B-98 ALIGN=MIDDLE  ALT=\"%289x%2B-14x%29%2B%28-6y%2B6y%29=78%2B-98\"   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=-5x%2B0y=-20 ALIGN=MIDDLE  ALT=\"-5x%2B0y=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=-20 ALIGN=MIDDLE  ALT=\"-5x=-20\"   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=%28-20%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"x=%28-20%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   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=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=9x-6y=78 ALIGN=MIDDLE  ALT=\"9x-6y=78\"   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=9%284%29-6y=78 ALIGN=MIDDLE  ALT=\"9%284%29-6y=78\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=36-6y=78 ALIGN=MIDDLE  ALT=\"36-6y=78\"   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=-6y=78-36 ALIGN=MIDDLE  ALT=\"-6y=78-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   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=-6y=42 ALIGN=MIDDLE  ALT=\"-6y=42\"   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=%2842%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y=%2842%29%2F%28-6%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;\" > 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=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\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=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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(4,-7\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(4,-7\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-6%2C14%2C-17%2C3%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-6%2C14%2C-17%2C3%2C%2826-3x%29%2F%28-2%29%2C%28-49%2B7x%29%2F%283%29%29%2C%0D%0Acircle%284%2C-7%2C0.05%29%2C%0D%0Acircle%284%2C-7%2C0.08%29%2C%0D%0Acircle%284%2C-7%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=3x-2y=26 ALIGN=MIDDLE  ALT=\"3x-2y=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x%2B3y=-49 ALIGN=MIDDLE  ALT=\"-7x%2B3y=-49\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) \r<BR>\n" );
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document.write( "================================================================\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Let's solve this system by 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%284x-5y=14%2C-12x%2B15y=-42%29 ALIGN=MIDDLE  ALT=\"system%284x-5y=14%2C-12x%2B15y=-42%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=3%284x-5y%29=3%2814%29 ALIGN=MIDDLE  ALT=\"3%284x-5y%29=3%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-15y=42 ALIGN=MIDDLE  ALT=\"12x-15y=42\"   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%2812x-15y=42%2C-12x%2B15y=-42%29 ALIGN=MIDDLE  ALT=\"system%2812x-15y=42%2C-12x%2B15y=-42%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=%2812x-15y%29%2B%28-12x%2B15y%29=%2842%29%2B%28-42%29 ALIGN=MIDDLE  ALT=\"%2812x-15y%29%2B%28-12x%2B15y%29=%2842%29%2B%28-42%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=%2812x%2B-12x%29%2B%28-15y%2B15y%29=42%2B-42 ALIGN=MIDDLE  ALT=\"%2812x%2B-12x%29%2B%28-15y%2B15y%29=42%2B-42\"   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=0 ALIGN=MIDDLE  ALT=\"0x%2B0y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   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=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>always</b></font> true, this means that there are an infinite number of solutions. \r<BR>\n" );
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document.write( "So the system is consistent and dependent.\r<BR>\n" );
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document.write( "================================================================\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "\n" );
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%28-2x%2B6y=19%2C10x-30y=-15%29 ALIGN=MIDDLE  ALT=\"system%28-2x%2B6y=19%2C10x-30y=-15%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%28-2x%2B6y%29=5%2819%29 ALIGN=MIDDLE  ALT=\"5%28-2x%2B6y%29=5%2819%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x%2B30y=95 ALIGN=MIDDLE  ALT=\"-10x%2B30y=95\"   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%28-10x%2B30y=95%2C10x-30y=-15%29 ALIGN=MIDDLE  ALT=\"system%28-10x%2B30y=95%2C10x-30y=-15%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=%28-10x%2B30y%29%2B%2810x-30y%29=%2895%29%2B%28-15%29 ALIGN=MIDDLE  ALT=\"%28-10x%2B30y%29%2B%2810x-30y%29=%2895%29%2B%28-15%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=%28-10x%2B10x%29%2B%2830y%2B-30y%29=95%2B-15 ALIGN=MIDDLE  ALT=\"%28-10x%2B10x%29%2B%2830y%2B-30y%29=95%2B-15\"   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=80 ALIGN=MIDDLE  ALT=\"0x%2B0y=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=80 ALIGN=MIDDLE  ALT=\"0=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify.\r<BR>\n" );
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document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=80 ALIGN=MIDDLE  ALT=\"0=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>never</b></font> true, this means that there are no solutions. \r<BR>\n" );
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document.write( "So the system is inconsistent.<BR>\n" );
document.write( " </SPAN>\n" );
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