document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504909>Question 504909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a system of two linear equations that has .<BR>\n" );
document.write( "a) only one solution ,(5,1).<BR>\n" );
document.write( "b) an infinite number of solutions . <BR>\n" );
document.write( "c) no solution.<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 #339758 by </B><A HREF=/tutors/aboutme.mpl?userid=emargo19><B>emargo19(101)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=emargo19><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=339758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) only one solution ,(5,1) ****instead of (2,3)<BR>\n" );
document.write( "Lets use point slope intercept equation <BR>\n" );
document.write( "let's say the slope is -2.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-y1%29=m%28x-x1%29+ ALIGN=MIDDLE  ALT=\"%28y-y1%29=m%28x-x1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29=-2%28x-5%29 ALIGN=MIDDLE  ALT=\"%28y-1%29=-2%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=-2x%2B10 ALIGN=MIDDLE  ALT=\"y-1=-2x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B11 ALIGN=MIDDLE  ALT=\"y=-2x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Eq1\r<BR>\n" );
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document.write( "For next equation:<BR>\n" );
document.write( "Lets use point slope intercept equation <BR>\n" );
document.write( "let's say the slope is 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=2%28x-10%29 ALIGN=MIDDLE  ALT=\"y-1=2%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-9 ALIGN=MIDDLE  ALT=\"y=2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----Eq2\r<BR>\n" );
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document.write( "Next lets check\r<BR>\n" );
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document.write( "Lets substitute <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-9 ALIGN=MIDDLE  ALT=\"y=2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > in eq 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B11 ALIGN=MIDDLE  ALT=\"y=-2x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9=-2x%2B11 ALIGN=MIDDLE  ALT=\"2x-9=-2x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=11%2B9 ALIGN=MIDDLE  ALT=\"4x=11%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=20 ALIGN=MIDDLE  ALT=\"4x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next lets substitute x=5 in eq <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%285%29-9 ALIGN=MIDDLE  ALT=\"y=2%285%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-9 ALIGN=MIDDLE  ALT=\"y=10-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore eqs are <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B11 ALIGN=MIDDLE  ALT=\"y=-2x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Eq1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-9 ALIGN=MIDDLE  ALT=\"y=2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----Eq2\r<BR>\n" );
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document.write( "----------------------<BR>\n" );
document.write( "For NO SOLUTION\r<BR>\n" );
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document.write( "REmember:<BR>\n" );
document.write( "No solution happens when two graphs are parallel. It looks like this (0=7) <BR>\n" );
document.write( "To make lines Paralel we have to have equal slopes.\r<BR>\n" );
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document.write( "Lets use the point slope equation  <BR>\n" );
document.write( "Lets choose points (3,2) and slope as 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=4%28x-2%29 ALIGN=MIDDLE  ALT=\"y-3=4%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-8%2B3 ALIGN=MIDDLE  ALT=\"y=4x-8%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-5 ALIGN=MIDDLE  ALT=\"y=4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ----eq1\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Lets use the point slope equation  again <BR>\n" );
document.write( "This time lets choose points (2,1) and slope as 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=m%28x-2%29 ALIGN=MIDDLE  ALT=\"y-1=m%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-8%2B1 ALIGN=MIDDLE  ALT=\"y=4x-8%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-7 ALIGN=MIDDLE  ALT=\"y=4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----eq2\r<BR>\n" );
document.write( "\n" );
document.write( "Lets check:<BR>\n" );
document.write( "y=4x-5<BR>\n" );
document.write( "y=4x-7<BR>\n" );
document.write( "Substitute y=4x-7 in eq y=4x-5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-7=4x-5 ALIGN=MIDDLE  ALT=\"4x-7=4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4x=-5%2B7 ALIGN=MIDDLE  ALT=\"4x-4x=-5%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2 ALIGN=MIDDLE  ALT=\"0=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "c)infinite number of solutions <BR>\n" );
document.write( "All that you need to do here is to write an equation and make a second equation a multiple<BR>\n" );
document.write( "of the first equation. Example:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The first equation is y = 2x +1 ---eq1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The second equation is 2y = 4x + 2 ---eq2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This 2nd  equ  is just 2 times the 1st eq. <BR>\n" );
document.write( " So this makes both eq the same they will have the same graph(1 line on the graph. So, these two eqns will have an infinite number of common <BR>\n" );
document.write( "solns.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );