document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478339>Question 478339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having alot of trouble understanding the process of solving a system of equations by subsitution vs elimination. \r<BR>\n" );
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document.write( "Solve the system of equations by substitution.<BR>\n" );
document.write( "2x	 + 	y	 = 	9<BR>\n" );
document.write( "x	 &#8722; 	4y	 = 	9\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "Solve the system of equations by elimination.<BR>\n" );
document.write( "49x &#8722; 27y + 47	 = 	0<BR>\n" );
document.write( "14x &#8722; 45y + 30	 = 	0\r<BR>\n" );
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document.write( "? I would so appreciate a detailed explanation of both processes.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327758 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=327758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations by substitution.<BR>\n" );
document.write( "2x + y = 9<BR>\n" );
document.write( "x &#8722; 4y = 9 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Solve the 2nd equation for \"x\":<BR>\n" );
document.write( "x = 4y+9<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute for \"x\" in the 1st equation <BR>\n" );
document.write( "and solve for \"y\":<BR>\n" );
document.write( "2(4y+9) + y = 9<BR>\n" );
document.write( "8y+18+y = 9<BR>\n" );
document.write( "9y = -9<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Now, solve for \"x\":<BR>\n" );
document.write( "x = 4y+9<BR>\n" );
document.write( "x = 4*-1+9<BR>\n" );
document.write( "x = -4+9<BR>\n" );
document.write( "x = 5<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "and <BR>\n" );
document.write( "Solve the system of equations by elimination.<BR>\n" );
document.write( "49x &#8722; 27y + 47 = 0<BR>\n" );
document.write( "14x &#8722; 45y + 30 = 0 <BR>\n" );
document.write( "----<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "49x  - 27y = -47<BR>\n" );
document.write( "14x  - 45y = -30<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "You have a choice of eliminating the x terms<BR>\n" );
document.write( "or the y terms.<BR>\n" );
document.write( "To eliminate the x terms:<BR>\n" );
document.write( "Multiply thru 1st equation by 14<BR>\n" );
document.write( "Multiply thru 2nd equation by 49<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "14*49x  - 14*27y = 14*-47<BR>\n" );
document.write( "49*14x  - 49*45y = 49*-30<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Subtract the 2st equation from the 1nd and solve for \"y\":<BR>\n" );
document.write( "1827y = 812<BR>\n" );
document.write( "y = 4/9<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Solve for \"x\" using any of the equations that relate x and y:<BR>\n" );
document.write( "14x &#8722; 45y + 30 = 0<BR>\n" );
document.write( "14x - 45(4/9) = -30<BR>\n" );
document.write( "14x - 20 = -30<BR>\n" );
document.write( "14x = -10<BR>\n" );
document.write( "x = -5/7<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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