document.write( "Question 1011120: Solve the four equations simultaneously ,\r
\n" ); document.write( "\n" ); document.write( "2a+c=0
\n" ); document.write( "3a+2b+d=3
\n" ); document.write( "a+3b+c=2
\n" ); document.write( "b+d= -1
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Algebra.Com's Answer #626691 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Solve the four equations simultaneously\r\n" );
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document.write( "2a + c = 0          (1)\r\n" );
document.write( "3a + 2b + d = 3     (2)\r\n" );
document.write( "a + 3b + c = 2      (3)\r\n" );
document.write( "b + d = -1          (4)\r\n" );
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document.write( "Express c = -2a from (1) and substitute it into (3). You will get\r\n" );
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document.write( "a + 3b - 2a = 3,   or   \r\n" );
document.write( "-a + 3b = 2         (3')\r\n" );
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document.write( "Next, express d = -1 - b from(4) and substitute it into (2). You will get\r\n" );
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document.write( "3a + 2b + (-1 - b) = 3,   or\r\n" );
document.write( "3a + b  = 4         (2').\r\n" );
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document.write( "Now you have this system of two equation in two unknowns (3') and (2').\r\n" );
document.write( "To solve it, express b = 4 - 3a from (2') and substitute it into (3'). You will get\r\n" );
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document.write( "-a + 3*(4 - 3a) = 2  ----->  -a - 9a = 2 - 12  ----->  -10a = - 10  ----->  a = 1.\r\n" );
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document.write( "Then from (2')  b = 4 - 3a = 4 - 3 = 1.\r\n" );
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document.write( "Finally, from (1)  c = -2a = -2*1 = -2;\r\n" );
document.write( "         from (4)  d = -1 - b = -1 - 1 = -2.\r\n" );
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document.write( "Answer. a = 1; b = 1; c = -2; d = -2.\r\n" );
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