document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149711>Question 149711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could any one of you help me out in solving the below problem. I tried a lot, but failed.\r<BR>\n" );
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document.write( "ax + by = 4; ax^2 + by^2 = -3; ax^3 + by^3 = 2, <BR>\n" );
document.write( "then what is the value of (2x-1)(2y-1)?\r<BR>\n" );
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document.write( "Thanks.<BR>\n" );
document.write( "Trins </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109841 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These are called \"systems of equations\" when you have <BR>\n" );
document.write( "several equations with a certain number of unknowns.<BR>\n" );
document.write( "It is an absolute fact that the number of equations<BR>\n" );
document.write( "has to match the number of unknowns in order to find<BR>\n" );
document.write( "values (numbers) for all the unknowns. <BR>\n" );
document.write( "You have 3 equations and 4 unknowns, so you need 1 more<BR>\n" );
document.write( "equation to find what x,y,a, and b are. What you can<BR>\n" );
document.write( "find is x and y in terms of a and b. That would only<BR>\n" );
document.write( "be 2 unknowns. I'm not sure if that is what's being asked for.<BR>\n" );
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document.write( "The other big thing to what for is systems of <BR>\n" );
document.write( "equations that don't give you answers at all, like<BR>\n" );
document.write( "(1)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4x ALIGN=MIDDLE  ALT=\"y+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+8x ALIGN=MIDDLE  ALT=\"2y+=+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+=+16x ALIGN=MIDDLE  ALT=\"4y+=+16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These are the same equation repeated 3 times<BR>\n" );
document.write( "Divide both sides of (2) by 2 and you get (1)<BR>\n" );
document.write( "Divide both sides of (3) by 4 and you also get (1)<BR>\n" );
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document.write( "Also there are systems that just have no intersections<BR>\n" );
document.write( "and can't be solved, like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x ALIGN=MIDDLE  ALT=\"y+=+-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+10x+%2B+25 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+10x+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll plot these:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C-x%2C+x%5E2+-+10x+%2B+25%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C-x%2C+x%5E2+-+10x+%2B+25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );