document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33798>Question 33798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a systems of equations problem and I need to solve for x,y,z.  I do not how to get any of the variables or what steps to take to get the answers.<BR>\n" );
document.write( "The problem:<BR>\n" );
document.write( "2x-5y+ ___=-22<BR>\n" );
document.write( "__+y+3z=10<BR>\n" );
document.write( "x+___+8z=15\r<BR>\n" );
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document.write( "The underscores represents blanks or O\r<BR>\n" );
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document.write( "If this had to be an augmented matrix, how would I do that and get those variables? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20202 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x-5y+ ___=-22...........................I<BR>\n" );
document.write( "__+y+3z=10.....................II<BR>\n" );
document.write( "x+___+8z=15...........................III\r<BR>\n" );
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document.write( "2*EQN.III-EQN.I<BR>\n" );
document.write( "2X+16Z-2X+5Y=30+22=52<BR>\n" );
document.write( "5Y+16Z=52...........................IV<BR>\n" );
document.write( "EQN.IV-5*EQN.II<BR>\n" );
document.write( "5Y+16Z-5Y-15Z=52-50=2<BR>\n" );
document.write( "Z=2....SUBSTITUTING IN EQN.III<BR>\n" );
document.write( "X+8*2=15<BR>\n" );
document.write( "X=15-16=-1<BR>\n" );
document.write( "SUBSTITUTING FOR Z IN EQN.II<BR>\n" );
document.write( "Y+3*2=10<BR>\n" );
document.write( "Y=10-6=4\r<BR>\n" );
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document.write( "USING MATRIX METHOD...AUGMENTED MATRIX IS \r<BR>\n" );
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document.write( "2	-5	0	-22		1	0	0	?<BR>\n" );
document.write( "0	1	3	10		0	1	0	?<BR>\n" );
document.write( "1	0	8	15		0	0	1	?\r<BR>\n" );
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document.write( "NR1=R1/2								\r<BR>\n" );
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document.write( "1	-2.5	0	-11					<BR>\n" );
document.write( "0	1	3	10					<BR>\n" );
document.write( "1	0	8	15					<BR>\n" );
document.write( "								<BR>\n" );
document.write( "NR3=R3-R1								<BR>\n" );
document.write( "			<BR>\n" );
document.write( "1	-2.5	0	-11<BR>\n" );
document.write( "0	1	3	10<BR>\n" );
document.write( "0	2.5	8	26<BR>\n" );
document.write( "			<BR>\n" );
document.write( "NR3=R3-2.5*R2			<BR>\n" );
document.write( "			<BR>\n" );
document.write( "1	-2.5	0	-11<BR>\n" );
document.write( "0	1	3	10<BR>\n" );
document.write( "0	0	0.5	1<BR>\n" );
document.write( "			<BR>\n" );
document.write( "NR3=R3/0.5			<BR>\n" );
document.write( "			<BR>\n" );
document.write( "1	-2.5	0	-11<BR>\n" );
document.write( "0	1	3	10<BR>\n" );
document.write( "0	0	1	2<BR>\n" );
document.write( "			<BR>\n" );
document.write( "NR2=R2-3R3			<BR>\n" );
document.write( "			<BR>\n" );
document.write( "1	-2.5	0	-11<BR>\n" );
document.write( "0	1	0	4<BR>\n" );
document.write( "0	0	1	2\r<BR>\n" );
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document.write( "NR1=R1+2.5R2			<BR>\n" );
document.write( "			<BR>\n" );
document.write( "1	0	0	-1<BR>\n" );
document.write( "0	1	0	4<BR>\n" );
document.write( "0	0	1	2<BR>\n" );
document.write( "			<BR>\n" );
document.write( "HENCE 			<BR>\n" );
document.write( "X=-1			<BR>\n" );
document.write( "Y=4			<BR>\n" );
document.write( "Z=2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );