document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15907>Question 15907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve this problem using substitution?<BR>\n" );
document.write( " X + Y-Z=3<BR>\n" );
document.write( "-3X   +Z=-5<BR>\n" );
document.write( " X +2Y-Z=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7849 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\" size = 2><b><BR>\n" );
document.write( "` X +` Y - Z =` 3<BR>\n" );
document.write( "-3X ` ` `+ Z = -5<BR>\n" );
document.write( "` X + 2Y - Z =` 3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Here are the seven steps.<BR>\n" );
document.write( "1. Pick a letter.  (If one of the equations has only two letters, choose the<BR>\n" );
document.write( "` `letter that is missing)<BR>\n" );
document.write( "2. Pick an equation that contains that letter<BR>\n" );
document.write( "3. Solve for that letter in that equation.<BR>\n" );
document.write( "4. Substitute what you get into any other equations that contains that letter,<BR>\n" );
document.write( "` `and simplify.<BR>\n" );
document.write( "5. Now you have only two equations in one unknown<BR>\n" );
document.write( "6. Solve that system for the two letters they contain<BR>\n" );
document.write( "7. Substitute the values of those two letters in the result of step 3.<BR>\n" );
document.write( "`<BR>\n" );
document.write( " 1. Pick a letter.  (If one of the equations has only two letters, choose the<BR>\n" );
document.write( "   letter that is missing)<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<font color = \"red\">Since the second equation, -3X +Z=-5,  has no Y, we pick Y<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "2. Pick an equation that contains that letter<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "I pick the first equation <BR>\n" );
document.write( "X + Y - Z = 3<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "3. Solve for that letter in that equation.<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "X + Y - Z = 3<BR>\n" );
document.write( "` ` ` ` Y = 3 - X + Z<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "4. Substitute what you get into any other equations that contains <BR>\n" );
document.write( "` `that letter, and simplify.<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "The third equation, X + 2Y - Z = 3, contains Y, so replace Y by 3-X+Z<BR>\n" );
document.write( "in it and simplify<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` ` ` ` X + 2Y - Z = 3 <BR>\n" );
document.write( "X + 2(3 - X + Z) - Z = 3<BR>\n" );
document.write( "`X + 6 - 2X + 2Z - Z = 3<BR>\n" );
document.write( "` ` ` ` ` ` ` -X + Z = -3<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "5. Now you have only two equations in one unknown<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "These are<BR>\n" );
document.write( "`<BR>\n" );
document.write( "-3X + Z = -5 and -X + Z = -3<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "6. Solve that system for the two letters they contain.<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "-3X + Z = -5<BR>\n" );
document.write( "`-X + Z = -3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Solve for Z in the second one just above,<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` ` Z = -3 + X<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Substitute -3+X for Z in the first one just above<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` ` `-3X + Z = -5 <BR>\n" );
document.write( "-3X + (-3 + X) = -5<BR>\n" );
document.write( "` `-3X - 3 + X = -5<BR>\n" );
document.write( "` ` ` ` ` `-2X = -2<BR>\n" );
document.write( "` ` ` ` ` ` `X = 1 <BR>\n" );
document.write( "`<BR>\n" );
document.write( "Substitute 1 for X in Z = -3 + X<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Z = -3 + (1) = -3 + 1 = -2<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "7. Substitute the values of those two letters in the result of step 3.<BR>\n" );
document.write( "`<font color = \"red\"><BR>\n" );
document.write( "Substitute 1 for X and -5 for Z in Y = 3 - X + Z<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Y = 3 - X + Z<BR>\n" );
document.write( "Y = 3 - (1) + (-2)<BR>\n" );
document.write( "Y = 3 - 1 - 2<BR>\n" );
document.write( "Y = 0<BR>\n" );
document.write( "`</font><BR>\n" );
document.write( "Edwin<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );