document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282696>Question 282696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me get started solving this equation:\r<BR>\n" );
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document.write( "4/3x + 2y = 6\r<BR>\n" );
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document.write( "I know you need to get a common denominator but I am not sure how this works with a fraction like 4/3x involved.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205248 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sorry there is not one unique solution. <BR>\n" );
document.write( "This is one equation with two variables (unknowns).<BR>\n" );
document.write( "To solve we need one equation for each unknown.<BR>\n" );
document.write( "To solve an equation means to find the value of the variables.<BR>\n" );
document.write( "Now  it appears that you don't really want to solve the equations but you want to know if the lines are parallel or perpendicular or neither.<BR>\n" );
document.write( "What is the full original problem as given by the teacher or the book?<BR>\n" );
document.write( "1/2x - y/3 = 2<BR>\n" );
document.write( "4/3x + 2y = 6<BR>\n" );
document.write( "They are not parallel. They do cross at x = 13/54, y = 3/13<BR>\n" );
document.write( "Now the question is whether they are perpendicular.<BR>\n" );
document.write( "For that we do need the slopes<BR>\n" );
document.write( "we can find the slope when the equation is in the form y=mx+b<BR>\n" );
document.write( "or while it is the standard form ax+by+c=0<BR>\n" );
document.write( "They are both in standard form<BR>\n" );
document.write( "first a=1/2 and b=-1/3<BR>\n" );
document.write( "-a/b<BR>\n" );
document.write( "-1/2/-1/3=-1/2*-3=3/2=slope<BR>\n" );
document.write( "second<BR>\n" );
document.write( "a=4/3 and b=2<BR>\n" );
document.write( "-a/b=<BR>\n" );
document.write( "-4/3/2=-4/3*1/2=-2/3 =slope<BR>\n" );
document.write( "-2/3*3/2=-1<BR>\n" );
document.write( "They are perpendicular since the product of the slopes is -1.<BR>\n" );
document.write( " </SPAN>\n" );
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