document.write( "Question 1060073: Solve the system of equations. (If the system is dependent, enter a general solution in terms of c. If there is no solution, enter NO SOLUTION.)\r
\n" ); document.write( "\n" ); document.write( "2x − y + z = 12
\n" ); document.write( "2y − 3z = −16
\n" ); document.write( "3y + 2z = 2
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Algebra.Com's Answer #675091 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Solve the system of equations.
\n" ); document.write( "(If the system is dependent, enter a general solution in terms of c.
\n" ); document.write( "If there is no solution, enter NO SOLUTION.)\r
\n" ); document.write( "\n" ); document.write( "2x − y + z = 12
\n" ); document.write( "2y − 3z = −16
\n" ); document.write( "3y + 2z = 2
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document.write( "2x -  y +  z =  12,    (1)\r\n" );
document.write( "     2y - 3z = -16,    (2)\r\n" );
document.write( "     3y + 2z =   2.    (3)\r\n" );
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document.write( "Notice that the equations (2) and (3) constitute a closed 2x2-sub-system.\r\n" );
document.write( "   (I use the term \"closed sub-system\" to highlight that these two equations are for two unknowns y and z and do not include \"x\".)\r\n" );
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document.write( "For it, multiply eq.(2) by 2 and eq(3) by 3, then add. You will get\r\n" );
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document.write( "4y + 9y + (-6z + 6z) = -32 + 6,   or\r\n" );
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document.write( "13y = -26  --->  y = -2.\r\n" );
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document.write( "Then from (3)  2z = 2 - 3y = 2 - 3*(-2) = 2 + 6 = 8  --->  z = 4.\r\n" );
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document.write( "Next, substitute the found values y and z into equation (1) and get x = 3.\r\n" );
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document.write( "Answer.  x= 3, y= -2, z= 4.\r\n" );
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