document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109682>Question 1109682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of 3 equations. Be sure to indicate which is your working equation and which is your focus variable. 2x+4y-z=1 and 3x+3y+4z=1 and -5x-8y+6z=5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724655 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) 2x +4y -z = 1<BR>\n" );
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document.write( "(2) 3x +3y +4z = 1<BR>\n" );
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document.write( "(3) -5x -8y +6z = 5<BR>\n" );
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document.write( "multiply equation 1 by 6 and add it to equation 3<BR>\n" );
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document.write( "(4) 7x +16y = 11<BR>\n" );
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document.write( "multiply equation 1 by 4 and add it to equation 2<BR>\n" );
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document.write( "(5) 11x +19y = 5<BR>\n" );
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document.write( "equations 4 and 5 are two equations in two unknowns<BR>\n" );
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document.write( "solve equation 4 for x<BR>\n" );
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document.write( "x = (11 -16y)/7<BR>\n" );
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document.write( "substitute for x in equation 5<BR>\n" );
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document.write( "11*((11 -16y)/7) +19y = 5<BR>\n" );
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document.write( "((121 -176y)/7) +19y = 5<BR>\n" );
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document.write( "multiply both sides of = by 7<BR>\n" );
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document.write( "121 -176y +133y = 35<BR>\n" );
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document.write( "-43y = -86<BR>\n" );
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document.write( "y = 2<BR>\n" );
document.write( "x = (11 -16(2))/7 = -3<BR>\n" );
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document.write( "use equation 1 to get the value for z<BR>\n" );
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document.write( "2(-3) +4(2) -z = 1<BR>\n" );
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document.write( "-6 +8 -z = 1<BR>\n" );
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document.write( "-z = -1<BR>\n" );
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document.write( "z = 1<BR>\n" );
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document.write( "x = -3, y = 2, z = 1<BR>\n" );
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document.write( "check answers by substituting in equations 1, 2 and 3<BR>\n" );
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document.write( "(1) 2(-3) +4(2) -1 = 1<BR>\n" );
document.write( "-6 +8 -1 = 1<BR>\n" );
document.write( "1 = 1<BR>\n" );
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document.write( "(2) 3(-3) +3(2) +4(1) = 1<BR>\n" );
document.write( "-9 +6 +4 = 1<BR>\n" );
document.write( "1 = 1<BR>\n" );
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document.write( "(3) -5(-3) -8(2) +6(1) = 5<BR>\n" );
document.write( "15 -16 +6 = 5<BR>\n" );
document.write( "5 = 5<BR>\n" );
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document.write( "the answer checks<BR>\n" );
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document.write( ": </SPAN>\n" );
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