document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172174>Question 172174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If possible, solve the system of equations. Use any method. If there is not unique solution to the system, state the reason\r<BR>\n" );
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document.write( "2x-9y=9       (1)<BR>\n" );
document.write( "-18x+81y= -81  (2)\r<BR>\n" );
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document.write( "What is the solution to this system?\r<BR>\n" );
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document.write( "Type an ordered pair. Type N if there is no solution. Type I if there is infinitely many solutions.\r<BR>\n" );
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document.write( "Which of the statements below is a good explanation for the solution?\r<BR>\n" );
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document.write( "The graphs intersect at one point, so the solution is unique.\r<BR>\n" );
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document.write( "The graphs of two equations represent the same line.\r<BR>\n" );
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document.write( "The graphs of the two equations never intersect.<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 #127220 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=127220\">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%282x-9y=9%2C-18x%2B81y=-81%29 ALIGN=MIDDLE  ALT=\"system%282x-9y=9%2C-18x%2B81y=-81%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=9%282x-9y%29=9%289%29 ALIGN=MIDDLE  ALT=\"9%282x-9y%29=9%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-81y=81 ALIGN=MIDDLE  ALT=\"18x-81y=81\"   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%2818x-81y=81%2C-18x%2B81y=-81%29 ALIGN=MIDDLE  ALT=\"system%2818x-81y=81%2C-18x%2B81y=-81%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=%2818x-81y%29%2B%28-18x%2B81y%29=%2881%29%2B%28-81%29 ALIGN=MIDDLE  ALT=\"%2818x-81y%29%2B%28-18x%2B81y%29=%2881%29%2B%28-81%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=%2818x%2B-18x%29%2B%28-81y%2B81y%29=81%2B-81 ALIGN=MIDDLE  ALT=\"%2818x%2B-18x%29%2B%28-81y%2B81y%29=81%2B-81\"   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. 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=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. So the system is consistent and dependent.\r<BR>\n" );
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document.write( "Graphically, these two equations are really the SAME equation. So this means that there are an infinite number of intersections. </SPAN>\n" );
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