document.write( "Question 56165: solve the system:
\n" ); document.write( "-32+3z=4(x-2y)
\n" ); document.write( "4(x-2y-z)=-36
\n" ); document.write( "-2(2x+y)+2z=-12 \n" ); document.write( "
Algebra.Com's Answer #38229 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A tedious looking problem which is no doubt created to torment young minds, however, on closer inspection we can see that it can be unravelled without too much difficulty.
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\n" ); document.write( "Get each equation in the ax + by + cz = d format:
\n" ); document.write( "Eq1:
\n" ); document.write( "32 + 3z = 4(x-2y)
\n" ); document.write( "32 + 3z = 4x - 8y
\n" ); document.write( "-4x + 8y + 3z = -32
\n" ); document.write( ":
\n" ); document.write( "Eq2:
\n" ); document.write( "4(x-2y-z) = -36
\n" ); document.write( "4x - 8y - 4z = -36
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\n" ); document.write( ":
\n" ); document.write( "Eq3:
\n" ); document.write( "-2(2x+y) + 2z = -12
\n" ); document.write( "-4x - 2y + 2z = -12
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\n" ); document.write( "Let's just deal with the 1st two equations; notice if we add them we will eliminate x and y, leaving us with the solution to z:
\n" ); document.write( ":
\n" ); document.write( "-4x + 8y + 3z = -32
\n" ); document.write( "4x - 8y - 4z = - 36
\n" ); document.write( "-------------------- add
\n" ); document.write( " 0x + 0y - 1z = -68
\n" ); document.write( "z = -68/-1
\n" ); document.write( "z = +68
\n" ); document.write( ":
\n" ); document.write( "Take eq 2 & 3, substitute 68 for z giving us two equations with two unknowns:
\n" ); document.write( "Eq2: 4x - 8y - 4z = -36 > > 4x - 8y - 4(68) = -36 > > 4x - 8y - 272 = -36
\n" ); document.write( "Eq3 -4x - 2y + 2z = -12 > > -4x - 2y + 2(68) = -12 > > -4x -2y + 136 = -12
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\n" ); document.write( "Combining the numbers:
\n" ); document.write( "4x - 8y = -36 + 272
\n" ); document.write( "-4x -2y = -12 - 136
\n" ); document.write( ":
\n" ); document.write( "We have two managable equations, adding them eliminates x, giving the y solution
\n" ); document.write( " 4x - 8y = + 236
\n" ); document.write( "-4x - 2y = - 148
\n" ); document.write( "---------------- add
\n" ); document.write( " 0x - 10y = + 88
\n" ); document.write( "y = +88/-10
\n" ); document.write( "y = - 8.8
\n" ); document.write( ":
\n" ); document.write( "Now we have y = -8.8 and z = + 68, almost done, let's substitute for y & z in the 3rd equation
\n" ); document.write( "-4x - 2y + 2z = -12
\n" ); document.write( "-4x - 2(-8.8) + 2(68) = -12
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\n" ); document.write( "-4x + 17.6 + 136 = -12
\n" ); document.write( "-4x = -12 - 17.6 - 136
\n" ); document.write( "-4x = -165.6
\n" ); document.write( " x = -165.6/-4
\n" ); document.write( " x = +41.4
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\n" ); document.write( "Did that help?\r
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