document.write( "Question 1028392: Hi I am so confused on how to work this because from my understanding, you can get rid of 2 letters when trying to find one. The three I have are 4x+5y+z=23, 2x-5y-z=-11, 3x+y+3z=-5. So far, all i have is x=2. Thank you! \n" ); document.write( "
Algebra.Com's Answer #643493 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
4x+5y+z=23,
\n" ); document.write( " 2x-5y-z=-11,
\n" ); document.write( " 3x+y+3z=-5.
\n" ); document.write( ":
\n" ); document.write( "When you know that x = 2, you substitute 2 for x in the equations then
\n" ); document.write( "You can choose a pair of equations to find the other variables
\n" ); document.write( "using the 2nd and 3rd equations
\n" ); document.write( "2(2) - 5y - z -11
\n" ); document.write( "4 - 5y -z = -11
\n" ); document.write( "-5y - z = -11 - 4
\n" ); document.write( "-5y - z = -15
\n" ); document.write( "and
\n" ); document.write( "3(2) + y +3z = -5
\n" ); document.write( "y + 3z = -5 - 6
\n" ); document.write( "y + 3z = -11
\n" ); document.write( "multiply the 1st equation by 3, add to the above equation
\n" ); document.write( "-15y -3z = -45
\n" ); document.write( " y + 3z = = -11
\n" ); document.write( "---------------
\n" ); document.write( "-14y + 0 = -56
\n" ); document.write( "y = -56/-14
\n" ); document.write( "y = +4
\n" ); document.write( "Now substitute 4 for y and find x using either of the two variable equations
\n" ); document.write( "-5(4) - z = -15
\n" ); document.write( "-20 - z = -15
\n" ); document.write( "-z = -15 + 20
\n" ); document.write( "-z = 5
\n" ); document.write( "z = -5
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check all three solution in the original equations \n" ); document.write( "
\n" );