document.write( "Question 110553: solve the system use the substitution method
\n" ); document.write( "2x-y-z=15
\n" ); document.write( "4x+5y+2z=10
\n" ); document.write( "-x-4y+3z=-20
\n" ); document.write( "please help don't understand it \n" ); document.write( "
Algebra.Com's Answer #80707 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
solve the system use the substitution method
\n" ); document.write( ":
\n" ); document.write( "Eq1: 2x - y - z = 1
\n" ); document.write( "Eq2: 4x +5y +2z = 10
\n" ); document.write( "Eq3: -x- 4y +3z =-20
\n" ); document.write( ":
\n" ); document.write( "Not sure why you would want to use the substitution method here. Elimination makes sense. But let's try to substitute and see what happens;
\n" ); document.write( "Using eq1:
\n" ); document.write( "2x - y - z = 1
\n" ); document.write( "-y = 1 - 2x + z
\n" ); document.write( "y = 2x - z - 1; make y positive multiply by -1
\n" ); document.write( ":
\n" ); document.write( "Substitute (2x-z-1) for y in Eq2
\n" ); document.write( "4x + 5(2x-z-1) + 2z = 10
\n" ); document.write( "4x + 10x - 5z - 5 + 2z = 10
\n" ); document.write( "14x - 3z = 10 + 5
\n" ); document.write( "14x - 3z = 15
\n" ); document.write( "-3z = -14x + 15
\n" ); document.write( "3z = 14x - 15
\n" ); document.write( "z = \"14%2F3\"x - 5
\n" ); document.write( ":
\n" ); document.write( "Substitute (2x-z-1) for y in Eq3
\n" ); document.write( "-x - 4(2x-z-1) + 3z = -20
\n" ); document.write( "-x - 8x + 4z + 4 + 3z = -20
\n" ); document.write( "-9x + 7z = -20 - 4
\n" ); document.write( "-9x + 7z = -24
\n" ); document.write( ":
\n" ); document.write( "Substitute (\"14%2F3\"x-5) for z in the above equation
\n" ); document.write( "-9x + 7(\"14%2F3\"x-5) = -24
\n" ); document.write( "-9x + \"98%2F3\"x - 35 = - 24
\n" ); document.write( "\"-27%2F3\"x + \"98%2F3\"x = - 24 + 35
\n" ); document.write( "\"71%2F3\"x = 11
\n" ); document.write( "x = 11*\"3%2F71\"
\n" ); document.write( "x = \"33%2F71\"
\n" ); document.write( "x = .46478; not even an integer, disgusting!
\n" ); document.write( ":
\n" ); document.write( "Using -9x + 7z = -24, substitute for x and find z:
\n" ); document.write( "-9(.46478) + 7z = -24
\n" ); document.write( "7z = -24 + 4.1831
\n" ); document.write( "z = -19.8169/7
\n" ); document.write( "z = -2.8309
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\n" ); document.write( "Find y using y = 2x - z - 1
\n" ); document.write( "y = 2(.46478) - (-2.8309) -1
\n" ); document.write( "y + .92956 + 2.8309 - 1
\n" ); document.write( "y = 2.76056
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\n" ); document.write( "All these solutions check out on the Ti83 Matrix function. Really a nasty problem, hope this helped you out. \r
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