document.write( "Question 1054759: solve using the substitution method
\n" ); document.write( "problem 2x-y-z=15
\n" ); document.write( " 4x+5y+2z=10
\n" ); document.write( " -x-4y+3z=-20\r
\n" ); document.write( "\n" ); document.write( "problem 4x+y+5z=-4
\n" ); document.write( " -3x+2y+4z=10
\n" ); document.write( " x-y-2z=-2\r
\n" ); document.write( "\n" ); document.write( "problem x+3y-z=12
\n" ); document.write( " 2x+4y-2z=6
\n" ); document.write( " -x-2y+z=-6 \n" ); document.write( "
Algebra.Com's Answer #671898 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "1. Solve any equation for any letter.\r\n" );
document.write( "2. Substitute what that letter equals for that letter in the \r\n" );
document.write( "other two equations and simplify.\r\n" );
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document.write( "[Now we'll have only a system in 2 equations and 2 letters]\r\n" );
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document.write( "3. Solve either equation for either letter.\r\n" );
document.write( "4. Substitute what that letter equals for that letter in the \r\n" );
document.write( "other equation in 2 letters and simplify.\r\n" );
document.write( "5. Substitute that in the other letter in one of the \r\n" );
document.write( "other equations in two letters and solve for a\r\n" );
document.write( "second letter.\r\n" );
document.write( "6. Finally substitute the numbers for the two letters\r\n" );
document.write( "you have in one of the original equations and solve\r\n" );
document.write( "for the last remaining letter:\r\n" );
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document.write( "(eq. 1)   2x -  y -  z =  15\r\n" );
document.write( "(eq. 2)   4x + 5y + 2z =  10\r\n" );
document.write( "(3q. 3)   -x - 4y + 3z = -20\r\n" );
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document.write( "1. Solve any equation for any letter.\r\n" );
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document.write( "I'll pick an easiest equation to solve for an easy letter.\r\n" );
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document.write( "Hmmm.  Think I'll pick eq. 1 to solve for, hmmm, y\r\n" );
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document.write( "(eq. 1)   2x -  y -  z =  15\r\n" );
document.write( "               -y      =  15 - 2x + z\r\n" );
document.write( "                y      = -15 + 2x - z\r\n" );
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document.write( "2. Substitute what that letter equals for that letter in the \r\n" );
document.write( "other two equations and simplify:\r\n" );
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document.write( "(eq. 2)   4x + 5y + 2z =  10\r\n" );
document.write( "          4x + 5(-15 + 2x - z) + 2z = 10\r\n" );
document.write( "          4x - 75 + 10x - 5z + 2z = 10\r\n" );
document.write( "          14x - 3z - 75 = 10\r\n" );
document.write( "(eq. 4)   14x - 3z = 85\r\n" );
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document.write( "(3q. 3)   -x - 4y + 3z = -20\r\n" );
document.write( "          -x - 4(-15 + 2x - z) +3z = -20\r\n" );
document.write( "          -x + 60 - 8x + 4z + 3z = -20\r\n" );
document.write( "          -9x + 7z + 60 = -20\r\n" );
document.write( "(eq. 5)   -9x + 7z = -80\r\n" );
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document.write( "Now we have only a system in 2 equations and 2 unknowns:\r\n" );
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document.write( "(eq. 4)   14x - 3z =  85\r\n" );
document.write( "(eq. 5)   -9x + 7z = -80\r\n" );
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document.write( "3. Solve either equation for either letter.\r\n" );
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document.write( "I'll pick the easier equation to solve for the easier letter.\r\n" );
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document.write( "(eq. 4)   14x - 3z =  85\r\n" );
document.write( "          -3z = 85 - 14x\r\n" );
document.write( "            z = -85/3 + (14/3)x\r\n" );
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document.write( "4. Substitute what that letter equals for that letter in the \r\n" );
document.write( "other equation and simplify:\r\n" );
document.write( "   \r\n" );
document.write( "(eq. 5)   -9x + 7z = -80\r\n" );
document.write( "          -9x + 7[-85/3 + (14/3)x] = -80\r\n" );
document.write( "          -9x - 595/3 + (98/3)x = -80\r\n" );
document.write( "          -27x - 595 + 98x = -240\r\n" );
document.write( "          71x - 595 = -240\r\n" );
document.write( "          71x = 355\r\n" );
document.write( "          x = 5\r\n" );
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document.write( "5. Substitute that in the other letter in one of the \r\n" );
document.write( "other equations in two letters and solve for a\r\n" );
document.write( "second letter:\r\n" );
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document.write( "I'll substitute x = 5 in eq. 5:\r\n" );
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document.write( "(eq. 5)   -9x + 7z = -80     \r\n" );
document.write( "          -9(5) + 7z = -80\r\n" );
document.write( "          -45 + 7z = -80\r\n" );
document.write( "          7z = =35\r\n" );
document.write( "           z = -5\r\n" );
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document.write( "6. Finally substitute the numbers for the two letters\r\n" );
document.write( "you have in one of the original equations and solve\r\n" );
document.write( "for the last remaining letter:\r\n" );
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document.write( "I'll pick eq. 3 to substitute x = 5 and z = -5 in\r\n" );
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document.write( "(3q. 3)   -x - 4y + 3z = -20\r\n" );
document.write( "          -(5) - 4y + 3(-5) = -20\r\n" );
document.write( "          -5 - 4y - 15 = -20\r\n" );
document.write( "          -4y - 20 = -20\r\n" );
document.write( "          -4y = 0\r\n" );
document.write( "            y = 0\r\n" );
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document.write( "Solution: (x,y,z) = (5,0,-5) \r\n" );
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document.write( "Follow those same steps in your second problem.\r\n" );
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document.write( "Answers are (x,y,z) = (-6,-20,8)\r\n" );
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document.write( "However your third problem is different. \r\n" );
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document.write( " x + 3y -  z = 12 \r\n" );
document.write( "2x + 4y - 2z =  6 \r\n" );
document.write( "-x - 2y +  z = -6\r\n" );
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document.write( "1. Solve any equation for any letter.\r\n" );
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document.write( "I'll pick the first to solve for x\r\n" );
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document.write( "x = 12 - 3y + z\r\n" );
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document.write( "2. Substitute what that letter equals for that letter in the \r\n" );
document.write( "other two equations and simplify.\r\n" );
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document.write( "2(12 - 3y + z) + 4y - 2z = 6\r\n" );
document.write( "24 - 6y + 2z + 4y - 2z = 6\r\n" );
document.write( "24 -2y = 6\r\n" );
document.write( "-2y = -18\r\n" );
document.write( "y = 9\r\n" );
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document.write( "-x - 2y +  z = -6\r\n" );
document.write( "-(12 - 3y + z) - 2y +  z = -6\r\n" );
document.write( "-12 + 3y - z - 2y +  z = -6\r\n" );
document.write( "-12 + y = -6\r\n" );
document.write( "y = 6\r\n" );
document.write( "  \r\n" );
document.write( "y cannot equal both 6 and 9.\r\n" );
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document.write( "So the system is inconsistent.  It has no solution.\r\n" );
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document.write( "Edwin
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