document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333422>Question 333422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the problem I have to solve it says I have to write a system of equations involving two equations in two variables then to solve the system. Here is the problem: Jean is twice as old as Michael. The sum of their ages 3 years ago was 45 years. Find their ages now. <BR>\n" );
document.write( "I tried to solve it without the sytem of equations and i got the answer of jean:32 and Michael:16 but then I realized I would get the question wrong if I didn't show the system of equations. Please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238919 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first, your answers, of Jean=32 and Michael 16, have you tested them to see if they are correct?   The sum of their ages 3 years ago was 45 years<BR>\n" );
document.write( "Let see, 3 years ago Jean=32-3=29, Michael=16-3=13 so their sum is 42, so your answers are incorrect!<BR>\n" );
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document.write( "Begin by letting J=Jean's age and M=Michaels age, you have two unknowns J and M<BR>\n" );
document.write( "and you need as many equations as unknowns.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Jean is twice as old as Michael<BR>\n" );
document.write( "J=2*M  [ this is your first equation ]<BR>\n" );
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document.write( "The sum of their ages 3 years ago was 45 years<BR>\n" );
document.write( "J-3 is jean's age 3 years ago<BR>\n" );
document.write( "M-3 is Michaels age 3 years ago,  so....<BR>\n" );
document.write( "(J-3) + (M-3)=45   [ this is your second equation]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "simplify the second equation<BR>\n" );
document.write( "(J-3) + (M-3)=45 <BR>\n" );
document.write( "J+M-6=45<BR>\n" );
document.write( "J+M=51\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "So now you have two equations and 2 unknowns<BR>\n" );
document.write( "There are many ways to solve this, substittution, elimination, matrices, graphing, guessing, cramer method, etc......<BR>\n" );
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document.write( "Try subtitution since the first equation is already set to one of the variables<BR>\n" );
document.write( "J =2*M<BR>\n" );
document.write( "substitute this into the second equation<BR>\n" );
document.write( "J+M=51<BR>\n" );
document.write( "(2*M)+M=51<BR>\n" );
document.write( "3*M=51<BR>\n" );
document.write( "M=51/3=17<BR>\n" );
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document.write( "So if M=17 and J=2*M then J=2*(17) =34<BR>\n" );
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document.write( "Check your answers\r<BR>\n" );
document.write( "\n" );
document.write( "go back to the original equations<BR>\n" );
document.write( "J=2M  and (J-3) + (M-3)=45 to see if M=17 and J=34 are valid<BR>\n" );
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