document.write( "Question 1023816: Solve the system by elimination.
\n" ); document.write( "4x+4y+z=24
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\n" ); document.write( "5x-4y-5z=12 \n" ); document.write( "

Algebra.Com's Answer #639321 by ikleyn(52873) $\"\"$ $\"About$

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\n" ); document.write( "Solve the system by elimination.
\n" ); document.write( "4x+4y+z=24
\n" ); document.write( "2x-4y+z=0
\n" ); document.write( "5x-4y-5z=12
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document.write( "4x + 4y + z  = 24,    (1)\r\n" );
document.write( "2x - 4y + z  =  0,    (2)\r\n" );
document.write( "5x - 4y - 5z = 12.    (3)\r\n" );
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document.write( "First, distract (1) from (2). Second, multiply (1) by 5 (both sides) and then add to (3). \r\n" );
document.write( "In this way you eliminate z and obtain the system for two unknowns x and y:\r\n" );
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document.write( "-2x -  8y = -24,      (4)\r\n" );
document.write( "25x + 16y = 132.      (5).\r\n" );
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document.write( "By continuing with the elimination method, multiply (4) by 2 (both sides) and then add to (5). You will get \r\n" );
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document.write( "21x = 132 - 48 = 84.\r\n" );
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document.write( "Hence, x =  = 4.\r\n" );
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document.write( "Next find y from (4) and then restore z from any of (1), (2) or (3).\r\n" );
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