document.write( "Question 1132744: A number plus half of another number equals 6; twice the first number minus three times the second number
\n" ); document.write( "equals 4. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #749866 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let these numbers be x and y.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The description means  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     +  = 6,         (1)\r\n" );
document.write( "\r\n" );
document.write( "    2x - 3y = 4.         (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply equation (1) by 2; keep equation (2) as is. You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    2x +  y = 12          (3)\r\n" );
document.write( "\r\n" );
document.write( "    2x - 3y = 4.          (4)    (which is the same as (2) )\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtract equation (4) from equation (3).  The terms \"2x\"  will cancel each other, and you will get a single equation for the unknown y:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       y - (-3y) = 12 - 4,     or\r\n" );
document.write( "\r\n" );
document.write( "       4y = 8                  =================>  y = 8/4 = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from equation (3)  you have 2x + 2 = 12  ====>  2x = 12 - 2 = 10  ====>  x = 10/2 = 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x= 5; y= 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution will be uncompleted until you CHECK it.\r\n" );
document.write( "\r\n" );
document.write( "Please do it on your own to make sure that my answer is correct.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In my solution, I used an elimination method, so you know now how it works.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "By the way, for your safety, ignore the solution and the answer by @josgarithmetic, since they are W R O N G.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );