document.write( "Question 1029385: Find the values of x and y for which the complex numbers
\n" ); document.write( "(2x+3y)+i(2y-1) and 10+i(5-x) are equal. \n" ); document.write( "

Algebra.Com's Answer #644425 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find the values of x and y for which the complex numbers
\n" ); document.write( "(2x+3y)+i(2y-1) and 10+i(5-x) are equal.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.\r\n" );
document.write( "\r\n" );
document.write( "It gives you two equations\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y = 10,    (1)\r\n" );
document.write( "2y-1    = 5-x.   (2)\r\n" );
document.write( "\r\n" );
document.write( "From (2), express x = 5 - 2y + 1 = 6 - 2y  and substitute it into (1). You will get \r\n" );
document.write( "\r\n" );
document.write( "2*(6-2y) + 3y = 10,\r\n" );
document.write( "\r\n" );
document.write( "12 - 4y + 3y = 10,\r\n" );
document.write( "\r\n" );
document.write( "-y = 10 - 12,\r\n" );
document.write( "\r\n" );
document.write( "-y = -2,\r\n" );
document.write( "\r\n" );
document.write( "y = 2.\r\n" );
document.write( "\r\n" );
document.write( "Then x = 6 - 2y = 6 - 2*2 = 6 - 4 = 2.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  x = 2,  y = 2.\r\n" );
document.write( "

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

\n" );