document.write( "Question 1124231: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller number minus 2 times the larger number is -6. Find the numbers \n" ); document.write( "

Algebra.Com's Answer #740579 by ikleyn(52781) $\"\"$ $\"About$

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

\r\n" );
document.write( "Let x be the smaller and y be the greater number.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then your system is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3x + 2y = 27,    (1)\r\n" );
document.write( "4x - 2y = -6.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve it, add the equations (both sides).  You will get\r\n" );
document.write( "\r\n" );
document.write( "3x + 4x = 27 - 6,    or\r\n" );
document.write( "\r\n" );
document.write( "7x = 21  ====>    x = 21/7 = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from eq(1),  2y = 27 - 3x = 27 - 3*3 = 18  and  y = 18/2 = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The smaller number is 3.  The greater number is 9.\r\n" );
document.write( "

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

\n" );