document.write( "Question 766025: Hello can you help me with this problem? It says you have to use the subsitution method to solve a system of equations that has three variables.\r
\n" ); document.write( "\n" ); document.write( "6x-4y+5z=31
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\n" ); document.write( "x+y+z=2\r
\n" ); document.write( "\n" ); document.write( "x=?
\n" ); document.write( "y=?
\n" ); document.write( "z=? \n" ); document.write( "

Algebra.Com's Answer #466640 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the substitution method to solve a
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document.write( "[1]           6x - 4y + 5z = 31\r\n" );
document.write( "[2]           5x + 2y + 2z = 13\r\n" );
document.write( "[3]            x +  y +  z =  2\r\n" );
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document.write( "Solve [3] for one of the letters.\r\n" );
document.write( "I'll pick z\r\n" );
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document.write( "[3]            x +  y +  z =  2\r\n" );
document.write( "[4]                      z =  2 - x - y\r\n" );
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document.write( "Using [4], Substitute 2 - x - y \r\n" );
document.write( "for z in [1]\r\n" );
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document.write( "[1]           6x - 4y + 5z = 31\r\n" );
document.write( "    6x - 4y + 5(2 - x - y) = 31\r\n" );
document.write( "    6x - 4y + 10 - 5x - 5y = 31\r\n" );
document.write( "               x - 9y + 10 = 31\r\n" );
document.write( "[5]                 x - 9y = 21\r\n" );
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document.write( "Using [4], Substitute 2 - x - y \r\n" );
document.write( "for z in [2]\r\n" );
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document.write( "[2]           5x + 2y + 2z = 13   \r\n" );
document.write( "    5x + 2y + 2(2 - x - y) = 13\r\n" );
document.write( "     5x + 2y + 4 - 2x - 2y = 13\r\n" );
document.write( "                    3x + 4 = 13\r\n" );
document.write( "                        3x = 9\r\n" );
document.write( "[6]                      x = 3\r\n" );
document.write( "Using [6], Substitute 3 \r\n" );
document.write( "for x in [5]\r\n" );
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document.write( "[5]                 x - 9y = 21\r\n" );
document.write( "                    3 - 9y = 21\r\n" );
document.write( "                       -9y = 18\r\n" );
document.write( "[7]                      y = -2\r\n" );
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document.write( "Using [6] and [7], Substitute 3 \r\n" );
document.write( "for x and -2 for y in [5] in [4]\r\n" );
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document.write( "[4]                      z = 2 - x - y\r\n" );
document.write( "                         z = 2 - 3 - (-2)\r\n" );
document.write( "                         z = 2 - 3 + 2\r\n" );
document.write( "[8]                      z = 1\r\n" );
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document.write( "Answer: \r\n" );
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document.write( "[6]                      x = 3\r\n" );
document.write( "[7]                      y = -2\r\n" );
document.write( "[8]                      z = 1\r\n" );
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document.write( "Edwin

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