document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144638>Question 144638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For problems1, 2, 3<BR>\n" );
document.write( "a. Tell whether the systems of equation have no solution, one solution or many solutions:\r<BR>\n" );
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document.write( "problem 1 - x+y-1<BR>\n" );
document.write( "            2x+2y=2\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "problem 2 -  x+y=1<BR>\n" );
document.write( "             x-y=1\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "problem 3 -  x+y=1<BR>\n" );
document.write( "             x+y=2\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "I have tried to solve thee many times, but I seem to come out with different answers each time.  Please help me.\r<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 #105431 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For each of your problems, solve both of the equations for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In other words, using the rules for manipulating equations, rearrange both equations in the problem so that each is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then compare the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > parts of each equation.\r<BR>\n" );
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document.write( "You will have two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m%5B1%5Dx%2Bb%5B1%5D ALIGN=MIDDLE  ALT=\"y=m%5B1%5Dx%2Bb%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m%5B2%5Dx%2Bb%5B2%5D ALIGN=MIDDLE  ALT=\"y=m%5B2%5Dx%2Bb%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D%3C%3Em%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D%3C%3Em%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your system has exactly one element in the solution set.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=m%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=m%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D%3C%3Eb%5B2%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D%3C%3Eb%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your system has an empty solution set.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=m%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=m%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=b%5B2%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D=b%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your system has many elements in the solution set, infinitely many, in fact. </SPAN>\n" );
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