document.write( "Question 1083879: Draw a Venn Diagram and use the given information to fill in the number of elements in each region. n(A)=24, n(B)=17 n(AUB)=32 and n(A')=11 \n" ); document.write( "

Algebra.Com's Answer #697934 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "  n(A) = 24 = x + y\r\n" );
document.write( "  n(B) = 17 = y + z\r\n" );
document.write( "n(AUB) = 32 = x + y + z\r\n" );
document.write( " n(A') = 11 = z + w \r\n" );
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document.write( "So the system of equations is:\r\n" );
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document.write( "(eq. 1)              x + y         = 24\r\n" );
document.write( "(eq. 2)                  y + z     = 17\r\n" );
document.write( "(eq. 3)              x + y + z     = 32\r\n" );
document.write( "(eq. 4)                      z + w = 11\r\n" );
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document.write( "Subtract (eq. 3) minus (eq. 1)\r\n" );
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document.write( " (eq. 3)              x + y + z     = 32\r\n" );
document.write( "-(eq. 1)             -x - y         =-24\r\n" );
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document.write( "                              z     =  8\r\n" );
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document.write( "Subtract (eq. 3) minus (eq. 2)\r\n" );
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document.write( " (eq. 3)              x + y + z     = 32\r\n" );
document.write( "-(eq. 2)                 -y - z     =-17\r\n" );
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document.write( "                      x             = 15\r\n" );
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document.write( "Substitute x = 15 in (eq. 1)\r\n" );
document.write( "(eq. 1)              15 + y         = 24  \r\n" );
document.write( "                          y         =  9\r\n" );
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document.write( "Substitute z = 8 in (eq. 4)\r\n" );
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document.write( "(eq. 4)                      z + w = 11\r\n" );
document.write( "                             8 + w = 11\r\n" );
document.write( "                                 w = 3\r\n" );
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document.write( "Edwin

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