document.write( "Question 1089714: Solve using Cramer's rule
\n" ); document.write( "x + y + z = a
\n" ); document.write( "x + 2y + 2z = a + b
\n" ); document.write( "x + 2y + 3z = a + b + c
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #704071 by ikleyn(52786) $\"\"$ $\"About$

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

\r\n" );
document.write( "x +  y +  z = a             (1)\r\n" );
document.write( "x + 2y + 2z = a + b         (2)\r\n" );
document.write( "x + 2y + 3z = a + b + c     (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The Cramer's rule is very bad choice as the method for solving this system.\r\n" );
document.write( "\r\n" );
document.write( "The best choice is the Elimination method. Using the Elimination method, first subtract eq(2) from eq(3). You will get\r\n" );
document.write( "\r\n" );
document.write( "z = c,     and one unknown is just found.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, multiply eq(1) by 2 and then write this modified eq(1) with eq(2) together:\r\n" );
document.write( "\r\n" );
document.write( "2x + 2y + 2z = 2a,          (4)\r\n" );
document.write( " x + 2y + 2z =  a + b       (5)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtract eq(5) from eq(4). You will get\r\n" );
document.write( "\r\n" );
document.write( "x = a - b,     and one more unknown is just found.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now substitute the found values (expressions) for x and z into equation (1). You will get\r\n" );
document.write( "\r\n" );
document.write( "(a-b) + y + c = a,\r\n" );
document.write( "\r\n" );
document.write( "which implies\r\n" );
document.write( "\r\n" );
document.write( "y = a - (a-b) - c = b - c.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  x = a - b;  y = b - c,  and  z = c.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );