document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622962>Question 622962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure if i did this right mind helping me out?<BR>\n" );
document.write( "Solve the system of equations<BR>\n" );
document.write( "{x+y+z=-3<BR>\n" );
document.write( "{x-y+3z=-13<BR>\n" );
document.write( "{4x+4y+4z=-15\r<BR>\n" );
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document.write( "My answer looks like this <BR>\n" );
document.write( "x=-2,y=3,z=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391755 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Here is how to check your answer. If you got it right, the values you found for x, y, and z will make every equation in the system true.<BR>\n" );
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document.write( "Just substitute -2 for x, 3 for y, and -4 for z in each equation.\r<BR>\n" );
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document.write( "x+y+z=-3<BR>\n" );
document.write( "(-2)+(3)+(-4)=-3<BR>\n" );
document.write( "-3=-3 <BR>\n" );
document.write( "Check!!<BR>\n" );
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document.write( "x-y+3z=-13<BR>\n" );
document.write( "(-2)-(3)+3(-4)=-13<BR>\n" );
document.write( "-2-3-12=-13<BR>\n" );
document.write( "-17=-13<BR>\n" );
document.write( "Oops...Your solution doesn't work in this equation.<BR>\n" );
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document.write( "x=-2,y=3,z=-4<BR>\n" );
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document.write( "We can see that there is a problem with your calculations because the solution must work in every equation.<BR>\n" );
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document.write( "Let's start with the elimination method. Multiply every term in  equation {A} by -4. <BR>\n" );
document.write( "{A} x+y+z=-3  ---------------> -4x-4y-4z=12<BR>\n" );
document.write( "{B} x-y+3z=-13<BR>\n" );
document.write( "{C} 4x+4y+4z=-15 -----------> 4x+4y+4z=-15<BR>\n" );
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document.write( "Add equations {A} and {C}<BR>\n" );
document.write( "-4x-4y-4z=12<BR>\n" );
document.write( "4x+4y+4z=-15<BR>\n" );
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document.write( "Since the variables all cancel out (-4x+4x=0, etc.) we have<BR>\n" );
document.write( "0=-3<BR>\n" );
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document.write( "This result tells us that these two equations have no points in common. In 2-D, this is analogous to parallel lines. Your system has no single point (x,y,z) solution.<BR>\n" );
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document.write( "Here are some pictures of what solutions to systems of equations with three variables can look like:<BR>\n" );
document.write( "http://www.mathwarehouse.com/algebra/planes/systems/three-variable-equations.php<BR>\n" );
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document.write( "Hope this helps! Feel free to email me if you have questions about this explanation.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );