document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167863>Question 167863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem is dealing with systems of linear equations in more than two variables. I have to solve each system of equations.  I have tried but can't seem to get the answer using the substitution or elimination method.\r<BR>\n" );
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document.write( "3x + 4y - z = -7<BR>\n" );
document.write( "x - 5y + 2z = 19<BR>\n" );
document.write( "5x + y - 2z = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123741 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x + 4y - z = -7<BR>\n" );
document.write( "x - 5y + 2z = 19<BR>\n" );
document.write( "5x + y - 2z = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add the 2nd and 3rd equations<BR>\n" );
document.write( "x - 5y + 2z = 19<BR>\n" );
document.write( "5x + y - 2z = 5<BR>\n" );
document.write( "------------------adding eliminates z<BR>\n" );
document.write( "6x - 4y = 24<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply 1st equation by 2, add to the 2nd equation<BR>\n" );
document.write( "6x + 8y - 2z = -14<BR>\n" );
document.write( "x -  5y + 2z = 19<BR>\n" );
document.write( "------------------Adding eliminates z again<BR>\n" );
document.write( "7x + 3y = 5<BR>\n" );
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document.write( "Two equation two unknowns:<BR>\n" );
document.write( "Multiply the 1st two unknown eq by 3 and the 2nd eq by 4, add<BR>\n" );
document.write( "18x - 12y  = 72<BR>\n" );
document.write( "28x + 12y  = 20<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "46x = 92<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92%2F46 ALIGN=MIDDLE  ALT=\"92%2F46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "Find y using 7x + 3y = 5<BR>\n" );
document.write( "7(2) + 3y = 5<BR>\n" );
document.write( "14 + 3y = 5<BR>\n" );
document.write( "3y = 5 - 14<BR>\n" );
document.write( "3y = -9<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%2F3 ALIGN=MIDDLE  ALT=\"%28-9%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -3<BR>\n" );
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document.write( "Find z using the 1st equation<BR>\n" );
document.write( "3x + 4y - z = -7<BR>\n" );
document.write( "3(2) + 4(-3) - z = -7<BR>\n" );
document.write( "6 - 12 - z = -7<BR>\n" );
document.write( "-6 - z = -7<BR>\n" );
document.write( "-z = -7 + 6<BR>\n" );
document.write( "-z = -1<BR>\n" );
document.write( "z = 1<BR>\n" );
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document.write( "Check solution on the 2nd equation:<BR>\n" );
document.write( "x - 5y + 2z = 19<BR>\n" );
document.write( "2 -5(-3) + 2(1) =<BR>\n" );
document.write( "2 + 15 + 2 = 19; confirms our solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );