document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976020>Question 976020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the system of equations:<BR>\n" );
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document.write( "                           x + ay = 4<BR>\n" );
document.write( "                           ax + 9y = b<BR>\n" );
document.write( "   (A) For which value of a does the above system of equation have a unique solution?<BR>\n" );
document.write( "   (B) Find the values of a and b for which the system has MORE THAN ONE set of solutions.\r<BR>\n" );
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document.write( "Please help me, I have tried everything. Please show the steps for the answer as well. Thank you<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 #597689 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=597689\">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=system%28x+%2B+ay+=+4%2C+ax+%2B+9y+=+b%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+ay+=+4%2C+ax+%2B+9y+=+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Their corresponding slopes are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-1%2Fa%2C-a%2F9%29 ALIGN=MIDDLE  ALT=\"system%28-1%2Fa%2C-a%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "UNIQUE SOLUTION?<BR>\n" );
document.write( "The slopes must be not equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fa%3C%3E-a%2F9 ALIGN=MIDDLE  ALT=\"-1%2Fa%3C%3E-a%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%3C%3Ea ALIGN=MIDDLE  ALT=\"-9%3C%3Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a can be ANY real number NOT equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the system will have ONE solution; but realize, another requirement is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3C%3E4 ALIGN=MIDDLE  ALT=\"b%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "MORE THAN ONE SOLUTION?<BR>\n" );
document.write( "Values for a are ANY real number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E-9 ALIGN=MIDDLE  ALT=\"a%3C%3E-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is that the two equations must be equivalent; they may look different but must satisfy the same line, have the same graph. </SPAN>\n" );
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