document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55038>Question 55038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two records and three tapes cost $31. Three records and two tapes cost $29. Find the cost of each record and each tape\r<BR>\n" );
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document.write( "Let's call x the cost of records and y the cost of tapes. As a side note, who really cares? Don't we all buy CDs if not MP3s now?\r<BR>\n" );
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document.write( "Anyway, the first sentance in math-speak says:<BR>\n" );
document.write( "2x + 3y = 31\r<BR>\n" );
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document.write( "And the second says\r<BR>\n" );
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document.write( "3x + 2y = 29\r<BR>\n" );
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document.write( "There are a few basic ways to tackle this problem:\r<BR>\n" );
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document.write( "a) Addition method<BR>\n" );
document.write( "b) Substitution method<BR>\n" );
document.write( "c) Matrix method. <BR>\n" );
document.write( "d) Graph method\r<BR>\n" );
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document.write( "I think I'm a fan of the substitution.\r<BR>\n" );
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document.write( "we'll take the first equation and solve for x\r<BR>\n" );
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document.write( "2x + 3y = 31<BR>\n" );
document.write( "Subtracting 3y from both sides gives<BR>\n" );
document.write( "2x = -3y + 31<BR>\n" );
document.write( "And divide by two.<BR>\n" );
document.write( "x = -3/2y + 31/2\r<BR>\n" );
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document.write( "Ok...now we take the second equation<BR>\n" );
document.write( "3x + 2y = 29<BR>\n" );
document.write( "and substitute x = -3/2y +31/2 in for x\r<BR>\n" );
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document.write( "3(-3/2y +31/2) +2y = 29\r<BR>\n" );
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document.write( "Now, we'll simplify the whole mess.<BR>\n" );
document.write( "-9/2y + 93/2 + 2y = 29\r<BR>\n" );
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document.write( "Combine like terms<BR>\n" );
document.write( "-5/2y + 93/2 = 29\r<BR>\n" );
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document.write( "Moving the 93/2 to the right side yields<BR>\n" );
document.write( "-5/2y = 58/2 - 93/2<BR>\n" );
document.write( "-5/2y = -35/2\r<BR>\n" );
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document.write( "dividing by -5/2 gives<BR>\n" );
document.write( "y = -35/2(-2/5)<BR>\n" );
document.write( "y = 7\r<BR>\n" );
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document.write( "Ok...y = 7! Let's sub that into one of our original equations and solve for x.\r<BR>\n" );
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document.write( "2x + 3(7)=31<BR>\n" );
document.write( "2x + 21 = 31<BR>\n" );
document.write( "2x = 10<BR>\n" );
document.write( "x=5\r<BR>\n" );
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document.write( "We've got x=5 and y = 7. Lets check our answers with the second equation just to make sure we've got it. \r<BR>\n" );
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document.write( "3(5) + 2(7) = 29<BR>\n" );
document.write( "15+14=29<BR>\n" );
document.write( "29=29 \r<BR>\n" );
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document.write( "Yep..we did it right!\r<BR>\n" );
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document.write( "Records are $5 and Tapes are $7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37260 by </B><A HREF=/tutors/aboutme.mpl?userid=Hook><B>Hook(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Hook><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=37260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call x the cost of records and y the cost of tapes. As a side note, who really cares? Don't we all buy CDs if not MP3s now?\r<BR>\n" );
document.write( "\n" );
document.write( "Anyway, the first sentance in math-speak says:<BR>\n" );
document.write( "2x + 3y = 31\r<BR>\n" );
document.write( "\n" );
document.write( "And the second says\r<BR>\n" );
document.write( "\n" );
document.write( "3x + 2y = 29\r<BR>\n" );
document.write( "\n" );
document.write( "There are a few basic ways to tackle this problem:\r<BR>\n" );
document.write( "\n" );
document.write( "a) Addition method<BR>\n" );
document.write( "b) Substitution method<BR>\n" );
document.write( "c) Matrix method. <BR>\n" );
document.write( "d) Graph method\r<BR>\n" );
document.write( "\n" );
document.write( "I think I'm a fan of the substitution.\r<BR>\n" );
document.write( "\n" );
document.write( "we'll take the first equation and solve for x\r<BR>\n" );
document.write( "\n" );
document.write( "2x + 3y = 31<BR>\n" );
document.write( "Subtracting 3y from both sides gives<BR>\n" );
document.write( "2x = -3y + 31<BR>\n" );
document.write( "And divide by two.<BR>\n" );
document.write( "x = -3/2y + 31/2\r<BR>\n" );
document.write( "\n" );
document.write( "Ok...now we take the second equation<BR>\n" );
document.write( "3x + 2y = 29<BR>\n" );
document.write( "and substitute x = -3/2y +31/2 in for x\r<BR>\n" );
document.write( "\n" );
document.write( "3(-3/2y +31/2) +2y = 29\r<BR>\n" );
document.write( "\n" );
document.write( "Now, we'll simplify the whole mess.<BR>\n" );
document.write( "-9/2y + 93/2 + 2y = 29\r<BR>\n" );
document.write( "\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "-5/2y + 93/2 = 29\r<BR>\n" );
document.write( "\n" );
document.write( "Moving the 93/2 to the right side yields<BR>\n" );
document.write( "-5/2y = 58/2 - 93/2<BR>\n" );
document.write( "-5/2y = -35/2\r<BR>\n" );
document.write( "\n" );
document.write( "dividing by -5/2 gives<BR>\n" );
document.write( "y = -35/2(-2/5)<BR>\n" );
document.write( "y = 7\r<BR>\n" );
document.write( "\n" );
document.write( "Ok...y = 7! Let's sub that into one of our original equations and solve for x.\r<BR>\n" );
document.write( "\n" );
document.write( "2x + 3(7)=31<BR>\n" );
document.write( "2x + 21 = 31<BR>\n" );
document.write( "2x = 10<BR>\n" );
document.write( "x=5\r<BR>\n" );
document.write( "\n" );
document.write( "We've got x=5 and y = 7. Lets check our answers with the second equation just to make sure we've got it. \r<BR>\n" );
document.write( "\n" );
document.write( "3(5) + 2(7) = 29<BR>\n" );
document.write( "15+14=29<BR>\n" );
document.write( "29=29 \r<BR>\n" );
document.write( "\n" );
document.write( "Yep..we did it right!\r<BR>\n" );
document.write( "\n" );
document.write( "Records are $5 and Tapes are $7 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );