document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123991>Question 123991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to solve each system by the addition method, and if a unique solution does not exist, state whether the system is inconsistent or dependent. I have no clue how to do these and I am hoping someone will help me. <BR>\n" );
document.write( "x+2y+z=2<BR>\n" );
document.write( "2x+3y+3z=-3<BR>\n" );
document.write( "2x+3y+2z=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90956 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=90956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + 2y + z = 2<BR>\n" );
document.write( "2x+ 3y +3z =-3<BR>\n" );
document.write( "2x+ 3y +2z = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "notice if you multiply the 2nd equation by -1, & add it to the 3rd equation<BR>\n" );
document.write( ":<BR>\n" );
document.write( "-2x - 3y -3z =+3<BR>\n" );
document.write( "2x +  3y +2z = 2<BR>\n" );
document.write( "------------------ adding eliminates both x & y, leaving us z<BR>\n" );
document.write( "0x + 0y - 1z = 5<BR>\n" );
document.write( "-z = 5<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "z = -5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute -5 for z in the 1st equation<BR>\n" );
document.write( "x + 2y - 5 = 2<BR>\n" );
document.write( "x + 2y = 2 + 5<BR>\n" );
document.write( "x + 2y = 7<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute -5 for z in the 2nd equation<BR>\n" );
document.write( "2x + 3y + 3(-5) = -3<BR>\n" );
document.write( "2x + 3y - 15 = -3<BR>\n" );
document.write( "2x + 3y = -3 + 15<BR>\n" );
document.write( "2x + 3y = +12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Now we can deal with 2 unknown equations to find x * y<BR>\n" );
document.write( "Multiply  eq: x +2y = 7 by -2 and add it to the above equation:<BR>\n" );
document.write( "-2x -4y = -14<BR>\n" );
document.write( " 2x +3y = +12<BR>\n" );
document.write( "---------------- adding eliminates x, find y<BR>\n" );
document.write( "0x - 1y = -2<BR>\n" );
document.write( "y = +2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find x using the 2nd equation, substitute for y and z:<BR>\n" );
document.write( "2x + 3y +3z =-3<BR>\n" );
document.write( "2x+ 3(2) + 3(-5) = -3<BR>\n" );
document.write( "2x + 6 - 15 = -3<BR>\n" );
document.write( "2x - 9 = -3 <BR>\n" );
document.write( "2x = -3 + 9<BR>\n" );
document.write( "2x = 6<BR>\n" );
document.write( "x = +3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in the 3rd equation<BR>\n" );
document.write( "2x+ 3y +2z = 2<BR>\n" );
document.write( "2(3) + 3(2) +2(-5) = <BR>\n" );
document.write( "6 + 6 - 10 = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Therefore we can say this system is dependent on:<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "z = -5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I know there are a lot steps, but none of them are complicated, try to study<BR>\n" );
document.write( "the procedure until it makes sense.  A<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );