document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116936>Question 1116936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Helping my son with some algebra stuff. We're struggling with systems of equations. What we're struggling with mostly is 'why' you do the order of operations in the way they are done. Here's the problem:<BR>\n" );
document.write( "a-6=2b<BR>\n" );
document.write( "a+b=15<BR>\n" );
document.write( "The questions calls for the point where the these equations cross (#,#)<BR>\n" );
document.write( "Here's where we are:<BR>\n" );
document.write( "Consolidating the problems: a+2b+a+b=6+15 or 2a+3b=21<BR>\n" );
document.write( "Using the basic y=Mx+b to get slope.<BR>\n" );
document.write( "Now have no clue where to go from here.<BR>\n" );
document.write( "Appreciate the help<BR>\n" );
document.write( "Robert & Jason </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731841 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=731841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The first step you took was an error, so go back to the beginning.  Since your equations are in \"a\" and \"b\", they represent lines on an \"ab\" coordinate plane rather than an \"xy\" coordinate plane.  The choice of which variable is on the horizontal axis and which is on the vertical is completely arbitrary and won't change the final outcome, so just for the sake of neatness, let's assume that ordered pairs in this plane will be represented in alphabetical order, that is to say a point in the plane, rather than being specified as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x,y)\"> will be specified as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a,b)\">\r<BR>\n" );
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document.write( "Given that, the first step is to specify each of your equations as b being a function of a, in other words, put them in the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ ma\ +\ i_b\">, where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i_b\"> is the b-axis intercept.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ 6\ =\ 2b\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ \frac{1}{2}a\ -\ 3\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ =\ 15\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ -a\ +\ 15\">\r<BR>\n" );
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document.write( "Since these two equations have different slope values, they must perforce intersect somewhere, and this is at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a,b)\"> where the values of a and b satisfy both equations.\r<BR>\n" );
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document.write( "Since we have two expressions in \"a\" that are equal to the variable b, set these two expressions equal to each other and solve for a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{2}a\ -\ 3\ =\ -a\ +\ 15\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ 6\ =\ -2a\ +\ 30\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3a\ =\ 36\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ 12\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ -12\ +\ 15\ =\ 3\">\r<BR>\n" );
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document.write( "Hence, the point of intersection is the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (12,3)\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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