document.write( "Question 682221: Hello I have to solve three equations with three variables
\n" ); document.write( "The equations are
\n" ); document.write( "6q-r+2s=8
\n" ); document.write( "2q+3r-s=-9
\n" ); document.write( "4q+2r+5s=1
\n" ); document.write( "I have the equations using the process of elimination to find x y and z
\n" ); document.write( "The problem is I've been on this question for more than an hour either getting decimals as my answers and or equations which I can't solve
\n" ); document.write( "Honestly I don't know what I'm doing wrong.Ive tried to eliminate the q's first but afterwards towards solving I got 2.5 which I know is wrong \n" ); document.write( "
Algebra.Com's Answer #423148 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
6q - r + 2s = 8
\n" ); document.write( "2q + 3r - s = -9
\n" ); document.write( "4q + 2r + 5s= 1
\n" ); document.write( ":
\n" ); document.write( "There are several ways to do this, sometimes it's helpful to slip \"substitution\" among the eliminations.
\n" ); document.write( ":
\n" ); document.write( "Multiply 1st eq by -1 and add to the other 2
\n" ); document.write( "-6q + r - 2s = -8
\n" ); document.write( "2q + 3r - s = -9
\n" ); document.write( "4q + 2r + 5s = 1
\n" ); document.write( "-------------------Adding eliminates q
\n" ); document.write( "6r + 2s = -16
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "3r + s = -8
\n" ); document.write( "s = -3r - 8
\n" ); document.write( ":
\n" ); document.write( "Taking the last two equations, multiply the middle equation by 2
\n" ); document.write( "4q + 6r - 2s = -18
\n" ); document.write( "4q + 2r + 5s = 1
\n" ); document.write( "---------------------Subtraction eliminates q
\n" ); document.write( "4r - 7s = -19
\n" ); document.write( "replace s with (-3r-8)
\n" ); document.write( "4r -7(-3r-8) = -19
\n" ); document.write( "4r + 21r + 56 = -19
\n" ); document.write( "25r = -19 - 56
\n" ); document.write( "25r = -75
\n" ); document.write( "r = -75/25
\n" ); document.write( "r = -3
\n" ); document.write( ":
\n" ); document.write( "Find s
\n" ); document.write( "s = -3(-3) - 8
\n" ); document.write( "s = 9 - 8
\n" ); document.write( "s = 1
\n" ); document.write( ":
\n" ); document.write( "Find q using the first equation
\n" ); document.write( "6q -r + 2s = 8,
\n" ); document.write( "replace r and s
\n" ); document.write( "6q -(-3) + 2(1) = 8
\n" ); document.write( "6q + 3 + 2 = 8
\n" ); document.write( "6q = 8 - 5
\n" ); document.write( "6q = 3
\n" ); document.write( "q = 3/6
\n" ); document.write( "q = .5 or 1/2
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "You can confirm this in the original equations \n" ); document.write( "
\n" );