document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936830>Question 936830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a 3 variable linear equation problem, that I am not sure how to combine to solve. The problem is to solve the system using linear combination method. Here are the three equations:\r<BR>\n" );
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document.write( "5x-4y+4z=18<BR>\n" );
document.write( "-x+3y-2z=0<BR>\n" );
document.write( "4x-2y+7z=3\r<BR>\n" );
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document.write( "I have combined the first and second problem to eliminate z, but I don't know what to do from there. \r<BR>\n" );
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document.write( "First I distibuted a scale of 2 to the second problem so that the z's would cancel out, and then I solved. \r<BR>\n" );
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document.write( "(2)-x+3y-2z=0<BR>\n" );
document.write( "-2x+6y-4z=0\r<BR>\n" );
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document.write( "    5x-4y+4z=18<BR>\n" );
document.write( "+  -2x+6y-4z=0<BR>\n" );
document.write( "__________________<BR>\n" );
document.write( "    3x+2y   =18<BR>\n" );
document.write( "Please help me eliminate another variable so I can solve the rest of the problem.<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 #570308 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=570308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5      	x		-4      	y	+	4      	z	=	18      			--------------				1<BR>\n" );
document.write( "-1      	x	+	3      	y		-2      	z	=	0      			--------------				2<BR>\n" );
document.write( "4      	x		-2      	y	+	7      	z	=	-3      			--------------				3<BR>\n" );
document.write( "																<BR>\n" );
document.write( "consider equation 1 &2				Eliminate	y											<BR>\n" );
document.write( "Multiply 1 by		3      					-5      									<BR>\n" );
document.write( "Multiply 2 by		4      					4      									<BR>\n" );
document.write( "we get																<BR>\n" );
document.write( "15      	x			-12      	y	+	12      	z	=	54						<BR>\n" );
document.write( "-4      	x		+	12      	y		-8      	z	=	0						<BR>\n" );
document.write( "Add the two																<BR>\n" );
document.write( "11      	x			0      	y	+	4      	z	=	54	-------------				4	<BR>\n" );
document.write( "consider equation 2 & 3				Eliminate	y											<BR>\n" );
document.write( "Multiply 2 by				2      												<BR>\n" );
document.write( "Multiply 3 by				3      												<BR>\n" );
document.write( "we get																<BR>\n" );
document.write( "-2      	x	+	6      	y		-4      	z	=	0      							<BR>\n" );
document.write( "12      	x		-6      	y	+	21      	z	=	-9      							<BR>\n" );
document.write( "Add the two																<BR>\n" );
document.write( "10      	x	+	0      	y	+	17      	z	=	-9      	-------------5				5		<BR>\n" );
document.write( "Consider (4) & (5)			Eliminate	x												<BR>\n" );
document.write( "Multiply 4 by				-10      												<BR>\n" );
document.write( "Multiply (5) by				11      												<BR>\n" );
document.write( "we get																<BR>\n" );
document.write( "-110      	x		-40      	z	=	-540      										<BR>\n" );
document.write( "110      	x	+	187      	z	=	-99      										<BR>\n" );
document.write( "Add the two																<BR>\n" );
document.write( "0      	x	+	147      	z	=	-639      										<BR>\n" );
document.write( "/	147      															<BR>\n" );
document.write( "z	=	-4 17/49														<BR>\n" );
document.write( "10      	x	+	17      	z=	-9      											<BR>\n" );
document.write( "10      	x		-73 44/49	=	-9      											<BR>\n" );
document.write( "			x	=	6 24/49											<BR>\n" );
document.write( "Plug x & z in eq (1)																<BR>\n" );
document.write( "5      	x		-4      	y	+	4      	z	=	18      			--------------				1<BR>\n" );
document.write( "	32 22/49		-4      	y		-17 19/49		=	18      							<BR>\n" );
document.write( "			-4      	y				=	2 46/49							<BR>\n" );
document.write( "				y	=				- 36/49							<BR>\n" );
document.write( "	x=	6 24/49	y=	- 36/49	z=	-4 17/49										<BR>\n" );
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