document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=334297>Question 334297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine if the following statement is always true.  If it is not, provide a counterexample.  If the mathematical operation* is defined for all numbers x and y as 2x+3y, then the operation * is commutative. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239512 by </B><A HREF=/tutors/aboutme.mpl?userid=tinbar><B>tinbar(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tinbar><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=239512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x*y=2x+3y<BR>\n" );
document.write( "y*x=2y+3x\r<BR>\n" );
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document.write( "clearly x*y does NOT satisfy y*x, therefore it is no commutative\r<BR>\n" );
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document.write( "let x=4, y=5<BR>\n" );
document.write( "then x*y=2(4)+3(5)=8+15=23\r<BR>\n" );
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document.write( "y*x=2(5)+3(4)=10+12=22\r<BR>\n" );
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document.write( "since x*y does not equal y*x, this counterexample shows this operation definition is not commutative.  </SPAN>\n" );
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