document.write( "Question 1043382: A+b=8,c-d=6,a+c=13,b+d=8. What are values of a,b,c and d \n" ); document.write( "

Algebra.Com's Answer #658542 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A+b=8,c-d=6,a+c=13,b+d=8. What are values of a,b,c and d
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "a + b        = 8,   (1)\r\n" );
document.write( "       c - d = 6,   (2)\r\n" );
document.write( "a +    c     = 13,  (3)\r\n" );
document.write( "    b    + d = 8.   (4)\r\n" );
document.write( "\r\n" );
document.write( "Add all four equations (1), (2), (3) and (4) (both sides). You will get\r\n" );
document.write( "\r\n" );
document.write( "2a + 2b + 2c = 8 + 6 + 13 + 8 = 35,   or\r\n" );
document.write( "\r\n" );
document.write( "a + b + c = 17.5.     (5)\r\n" );
document.write( "\r\n" );
document.write( "Now distract eq.(1) from eq.(5). You will get\r\n" );
document.write( "\r\n" );
document.write( "c = 17.5 - 8 = 9.5.\r\n" );
document.write( "\r\n" );
document.write( "Next distract eq.(3) from eq.(5). You will get\r\n" );
document.write( "\r\n" );
document.write( "b = 17.5 - 13 = 4.5.\r\n" );
document.write( "\r\n" );
document.write( "Finally, from (1)  a = 8-b = 8-4.5 = 3.5,  and  from (4)  d = 8-b = 8-4.5 = 3.5.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  a = 3.5,  b = 4.5,  c = 9.5,  d = 3.5.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "There is a (hidden) symmetry in these equations that helps to solve the system.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Close ideas work in other cases. See the lessons \r
\n" ); document.write( "\n" ); document.write( " - The tricks to solve some word problems with three and more unknowns using mental math \r
\n" ); document.write( "\n" ); document.write( " - Joint-work problems for 3 participants \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );