document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634643>Question 634643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations<BR>\n" );
document.write( "X – 3z = -5<BR>\n" );
document.write( "2x- y + 2z= 16<BR>\n" );
document.write( "7x – 3y -5z =19\r<BR>\n" );
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document.write( "can you walk me thru the steps please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399796 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=399796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations<BR>\n" );
document.write( "X – 3z = -5<BR>\n" );
document.write( "2x- y + 2z= 16<BR>\n" );
document.write( "7x – 3y -5z = 19 <BR>\n" );
document.write( "There is more than one way to solve this, but this is a pretty simple one.<BR>\n" );
document.write( "A combination of substitution and elimination.<BR>\n" );
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document.write( "Rearrange the 1st equation to use for substitution:<BR>\n" );
document.write( "x = (3z-5)<BR>\n" );
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document.write( "Multiply the 2nd equation by 3, subtract from the 3rd equation<BR>\n" );
document.write( "7x – 3y - 5z = 19<BR>\n" );
document.write( "6x - 3y + 6z = 48<BR>\n" );
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document.write( "x + 0 - 11z = -29<BR>\n" );
document.write( "Replace x with (3z-5) from the 1st equation<BR>\n" );
document.write( "(3z-5) - 11z =-29<BR>\n" );
document.write( "3z - 11z = -29 + 5<BR>\n" );
document.write( "-8z = - 24<BR>\n" );
document.write( "z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-24%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"%28-24%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "z = +3<BR>\n" );
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document.write( "Back to the 1st equation, replace z with 3<BR>\n" );
document.write( "x = 3(3) - 5<BR>\n" );
document.write( "x = 9 - 5<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "Use the original 2nd equation to find y, Replace x and z<BR>\n" );
document.write( "2x - y + 2z = 16<BR>\n" );
document.write( "2(4) - y + 2(3) = 16 <BR>\n" );
document.write( "8 - y + 6 = 16<BR>\n" );
document.write( "-y = 16 - 8 - 6<BR>\n" );
document.write( "-y = 2<BR>\n" );
document.write( "Y has to be positive, multiply both sides by -1<BR>\n" );
document.write( "y = -2<BR>\n" );
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document.write( "Our Solution: x=4; y=-2; z=3<BR>\n" );
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document.write( "Check these in the 3rd original equation<BR>\n" );
document.write( "7x – 3y -5z = 19 <BR>\n" );
document.write( "7(4) - 3(-2) - 5(3) = <BR>\n" );
document.write( "28 + 6 - 15 = 19; confirms our solutions </SPAN>\n" );
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