document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112533>Question 112533</A>: <I><SPAN STYLE=\"word-break: break-all;\"> im not sure if this is the topic for it but how do you find or do standard form with integer coefficients? \r<BR>\n" );
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document.write( "what are coefficients?  how do you find them?\r<BR>\n" );
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document.write( "example......<BR>\n" );
document.write( "-4y + 6x + 7 = 0<BR>\n" );
document.write( "y= -11x -4<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 #82072 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=82072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In mathematics, a coefficient is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2 ALIGN=MIDDLE  ALT=\"9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 9.\r<BR>\n" );
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document.write( "Integer coefficients are simply coefficients that are integers.\r<BR>\n" );
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document.write( "The standard form of a linear equation in two variables is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2Bby=c ALIGN=MIDDLE  ALT=\"ax%2Bby=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the standard for of a linear equation in n variables is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5Dx%5B1%5D%2Ba%5B2%5Dx%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B1%5Dx%5B1%5D%2Ba%5B2%5Dx%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5Dx%5Bn%5D=c ALIGN=MIDDLE  ALT=\"a%5Bn%5Dx%5Bn%5D=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you had a mess like this:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=4-9x%2F2 ALIGN=MIDDLE  ALT=\"-2y=4-9x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you wanted to put it in standard form with integer coefficients, then you would first put the terms in order, like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F2-2y=4 ALIGN=MIDDLE  ALT=\"9x%2F2-2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F2 ALIGN=MIDDLE  ALT=\"9x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides)\r<BR>\n" );
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document.write( "And then get rid of that pesky 2 in the x term coefficient denominator by multiplying both sides of the equation by 2, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-4y=8 ALIGN=MIDDLE  ALT=\"9x-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Et Voila!  By the way, the x-term coefficient in the original problem I just posed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F2 ALIGN=MIDDLE  ALT=\"9x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same thing as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F2%29x ALIGN=MIDDLE  ALT=\"%289%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One more thing that is perhaps not obvious.  If you have a simple variable, such as x in an equation, the coefficient is understood to be 1.  We generally don't bother to write 1x, although it wouldn't necessarily be incorrect to do so.  So in the second example that you provided the coefficient on the y term is 1.\r<BR>\n" );
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document.write( "Also, if there is no variable, like the 7 in your first example, or the -4 in your second example, the 7 and the -4 are refered to as the constant coefficients.\r<BR>\n" );
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document.write( "Ok, your turn.  Tell me the coefficients in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B6x%2B7=0 ALIGN=MIDDLE  ALT=\"-4y%2B6x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Super-double-plus-extra credit:  Tell me the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
document.write( "John </SPAN>\n" );
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