document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4561>Question 4561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! I can not figure out two problems. I am to determine whether the following system is consistent, inconsistent, or dependent. If the system is consistent, find the solution of the system.<BR>\n" );
document.write( "The first problem is :\r<BR>\n" );
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document.write( " 6x + 4y =8<BR>\n" );
document.write( " 9x + 6y =12\r<BR>\n" );
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document.write( "and the second problem is:\r<BR>\n" );
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document.write( " 2/3x + 3/4y =4<BR>\n" );
document.write( " 5/6x - 3/8y = -11/2\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 #2422 by </B><A HREF=/tutors/aboutme.mpl?userid=Abbey><B>Abbey(339)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Abbey><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=2422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6x + 4y =8<BR>\n" );
document.write( "9x + 6y =12\r<BR>\n" );
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document.write( "Multiply the second equation by 2/3:<BR>\n" );
document.write( "6x + 4y = 8<BR>\n" );
document.write( "6x + 4y = 8\r<BR>\n" );
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document.write( "These are identical so they are the same line!\r<BR>\n" );
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document.write( "Second problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F3+%2B+3y%2F4+=4 ALIGN=MIDDLE  ALT=\"2x%2F3+%2B+3y%2F4+=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F6+-+3y%2F8+=+-11%2F2 ALIGN=MIDDLE  ALT=\"5x%2F6+-+3y%2F8+=+-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since I don't want to work with fractions, I will:<BR>\n" );
document.write( "Multiply the first equation by 12 to clear the denominators<BR>\n" );
document.write( "Multiply the second equation by 24 to clear the denominators\r<BR>\n" );
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document.write( "8x + 9Y = 48<BR>\n" );
document.write( "20x- 9y = -132\r<BR>\n" );
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document.write( "Add them together:<BR>\n" );
document.write( "28x = -84<BR>\n" );
document.write( "Divide both sides by 28:<BR>\n" );
document.write( "x=3\r<BR>\n" );
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document.write( "substitute back into either equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283%29%2F3+%2B+3y%2F4+=4 ALIGN=MIDDLE  ALT=\"2%283%29%2F3+%2B+3y%2F4+=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Clear parentheses:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B+3y%2F4+=+4 ALIGN=MIDDLE  ALT=\"2%2B+3y%2F4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract 2 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2F4+=+2 ALIGN=MIDDLE  ALT=\"3y%2F4+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides by 4/3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8%2F3 ALIGN=MIDDLE  ALT=\"y=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check by putting x and y back into the second equation to validate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F6+-+3y%2F8+=+-11%2F2 ALIGN=MIDDLE  ALT=\"5x%2F6+-+3y%2F8+=+-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283%29%2F6-%283%2F8%29%2A%288%2F3%29=-11%2F2 ALIGN=MIDDLE  ALT=\"5%283%29%2F6-%283%2F8%29%2A%288%2F3%29=-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2-1=-11%2F2 ALIGN=MIDDLE  ALT=\"5%2F2-1=-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2-2%2F2=-11%2F2 ALIGN=MIDDLE  ALT=\"5%2F2-2%2F2=-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "this is not a true statement, so this problem has no solution.<BR>\n" );
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