document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203089>Question 1203089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x*y=2x-y find the value of y if y*(3*y)=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838368 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "In many other contexts, the asterisk or star symbol * indicates multiplication.<BR>\n" );
document.write( "Example: 2*3 = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, this problem has the star operator redefined as:<BR>\n" );
document.write( "x*y = 2x-y<BR>\n" );
document.write( "This is a user-defined operator.<BR>\n" );
document.write( "It is not to be confused with the multiplication symbol.<BR>\n" );
document.write( "So be careful not to assume that y*(3*y) turns into 3y^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's replace x with 3<BR>\n" );
document.write( "x*y = 2x-y<BR>\n" );
document.write( "3*y = 2(3)-y<BR>\n" );
document.write( "3*y = 6-y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means any time we see 3*y, we can replace it with 6-y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x*y = 2x-y<BR>\n" );
document.write( "x*(3*y) = 2x-(3*y)<BR>\n" );
document.write( "x*(3*y) = 2x-(6-y)<BR>\n" );
document.write( "x*(3*y) = 2x-6+y<BR>\n" );
document.write( "x*(3*y) = 2x+y-6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next we'll replace x with y so we end up with y*(3*y)<BR>\n" );
document.write( "x*(3*y) = 2x+y-6<BR>\n" );
document.write( "y*(3*y) = 2y+y-6<BR>\n" );
document.write( "y*(3*y) = 3y-6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're told that y*(3*y) = 6<BR>\n" );
document.write( "We'll use the previous equation and this given fact to solve for y.<BR>\n" );
document.write( "y*(3*y) = 6<BR>\n" );
document.write( "3y-6 = 6<BR>\n" );
document.write( "3y = 6+6<BR>\n" );
document.write( "3y = 12<BR>\n" );
document.write( "y = 12/3<BR>\n" );
document.write( "y = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: y = 4<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );