document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24428>Question 24428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this is my question: Determine whether the system has one solution,no solution, or many solutions: y=2/3x<BR>\n" );
document.write( "                             2x-y=-4\r<BR>\n" );
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document.write( "could somebody please explain how to get the answer? Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13010 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=13010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first equation is ambiguous!<BR>\n" );
document.write( "Is it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%2F3x ALIGN=MIDDLE  ALT=\"y+=+2%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >???<BR>\n" );
document.write( "Let's assume that it is the first case.\r<BR>\n" );
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document.write( "You can solve questions like this by graphing or algebraically.<BR>\n" );
document.write( "Let's look at the graphic solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%282%2F3%29x%2C2x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%282%2F3%29x%2C2x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The red line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The green line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%2B4 ALIGN=MIDDLE  ALT=\"y+=+2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the 2nd equation written in terms of y.\r<BR>\n" );
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document.write( "Now solve algebraically by substitution:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute this equation for y in the second equation.<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y+=+-4 ALIGN=MIDDLE  ALT=\"2x-y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-%282%2F3%29x+=+-4 ALIGN=MIDDLE  ALT=\"2x-%282%2F3%29x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x+=+-4 ALIGN=MIDDLE  ALT=\"%284%2F3%29x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the multiplicative inverse of 4/3 (that's 3/4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitute this value of x into either one of the two original equations and solve for y. Take the first equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29%28-3%29 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29%28-3%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+=+-2 ALIGN=MIDDLE  ALT=\"y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is only one solution, it is: (-3, -2) Compare this with the intersection point of the two lines on the graph.\r<BR>\n" );
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document.write( "Now assume that the first equation is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%2F3x ALIGN=MIDDLE  ALT=\"y+=+2%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and let's look at the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C2%2F%283x%29%2C2x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C2%2F%283x%29%2C2x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As you can see, there would be two solutions (points of intersection) in this case. </SPAN>\n" );
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