document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75571>Question 75571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 50.Solve the system by substitution.<BR>\n" );
document.write( "	3x + 3y = 9<BR>\n" );
document.write( "	y = 2x – 12\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54211 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x + 3y = 9<BR>\n" );
document.write( "y = 2x – 12<BR>\n" );
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document.write( "From the bottom equation, you know what y (the left side) is in terms of x (the right side<BR>\n" );
document.write( "of the equation). So you can use the right side of the bottom equation as a replacement<BR>\n" );
document.write( "for y in the top equation.  When you make that substitution, the top equation becomes:<BR>\n" );
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document.write( "3x + 3(2x - 12) = 9<BR>\n" );
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document.write( "Multiply out the left side to get:<BR>\n" );
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document.write( "3x + 6x - 36 = 9<BR>\n" );
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document.write( "combine the x terms:<BR>\n" );
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document.write( "9x - 36 = 9<BR>\n" );
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document.write( "Add 36 to both sides to eliminate the -36 on the left side, and you get:<BR>\n" );
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document.write( "9x = 9 + 36 <BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "9x = 45<BR>\n" );
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document.write( "Solve for x by dividing both sides by 9 and you get:<BR>\n" );
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document.write( "x = 5<BR>\n" );
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document.write( "And from the bottom equation you know that y = 2x - 12. Substitute 5 for x and the equation<BR>\n" );
document.write( "becomes y = 2*5 - 12 = 10 - 12 = -2<BR>\n" );
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document.write( "So the answer to your problem is that for the two given equations, (5, -2) is a common solution<BR>\n" );
document.write( "meaning that x = 5, y = 2 is a common point whose values will make both of the given equations<BR>\n" );
document.write( "true.  <BR>\n" );
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document.write( "The rule for finding the common solution to a pair of linear equations begins with solving<BR>\n" );
document.write( "one of the two equations for a variable in terms of the other variable.  In this problem<BR>\n" );
document.write( "that was already done for you in the bottom equation.  Then you substitute that  solution<BR>\n" );
document.write( "into the other equation and solve for the one variable.  Then simply substitute that known<BR>\n" );
document.write( "value into either of the original equations and solve for the other variable.<BR>\n" );
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document.write( "Hope that helps you to understand how to proceed with a problem such as this. <BR>\n" );
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