document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203642>Question 203642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the following is known about three numbers: if the second number is subtracted from the sum of the first number and 5 times the third number, the result is -7. the third number plus 5 times the first number is -1. the first number plus 3 times the second number plus the third number is 5. find the three numbers. <BR>\n" );
document.write( "[hint: let x represent the first number, y the second number, and z the third number. use the given conditions to write and solve a system of equations.] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153643 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the following is known about three numbers: x, y, z<BR>\n" );
document.write( "if the second number is subtracted from the sum of the first number and 5 times the third number, the result is -7. <BR>\n" );
document.write( "(x+5z)-y = -7<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "the third number plus 5 times the first number is -1.<BR>\n" );
document.write( "z+5x = -1<BR>\n" );
document.write( "---------------------- <BR>\n" );
document.write( "the first number plus 3 times the second number plus the third number is 5. find the three numbers.<BR>\n" );
document.write( "x+3y+z = 5<BR>\n" );
document.write( " <BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Rearrange to get:<BR>\n" );
document.write( "x  - y + 5z = -7<BR>\n" );
document.write( "5x + 0y +z = -1<BR>\n" );
document.write( "x + 3y + z = 5<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Multiply thru the 1st equation by 3<BR>\n" );
document.write( "3x - 3y + 15z = -21<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Add that to the 3rd equation to get:<BR>\n" );
document.write( "4x +16z = -16<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Group that with the 2nd equation to solve for x and z:<BR>\n" );
document.write( "5x +  z = -1<BR>\n" );
document.write( "4x +16z = -16<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Multiply thru the 1st equation by 16; then solve for \"x\":<BR>\n" );
document.write( "80x + 16z = -16<BR>\n" );
document.write( "4x  + 16z =  -16<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Subtract the 2nd from the 1st to get:<BR>\n" );
document.write( "76x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute that into 4x+16z = -16 to get:<BR>\n" );
document.write( "z = -1<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Substitute those values  into x-y+5z = -7 to solve for \"y\":<BR>\n" );
document.write( "0 -y +5(-1)=-7<BR>\n" );
document.write( "-y-5=-7<BR>\n" );
document.write( "-y = -2<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "z = -1<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );