document.write( "Question 1003807: for what values of m and n is (5,-3) the solution for (x,y)?
\n" ); document.write( "The equations being: \r
\n" ); document.write( "\n" ); document.write( "mx-y=23
\n" ); document.write( "nx+y=12\r
\n" ); document.write( "\n" ); document.write( "Can you please explain this question?
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #620431 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
for what values of m and n is (5,-3) the solution for (x,y)?\r
\n" ); document.write( "\n" ); document.write( "The equations being:
\n" ); document.write( "
\r\n" );
document.write( "\"system%28mx-y=23%2Cnx%2By=12%29\"\r\n" );
document.write( "\r\n" );
document.write( "We substitute (5,-3) for (x,y) in both equations:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28m%285%29-%28-3%29=23%2Cn%285%29%2B%28-3%29=12%29\"\r\n" );
document.write( "\r\n" );
document.write( "Simplify them:\r\n" );
document.write( "\r\n" );
document.write( "\"system%285m%2B3=23%2C5n-3=12%29\"\r\n" );
document.write( "\r\n" );
document.write( "Simplify further:\r\n" );
document.write( "\r\n" );
document.write( "\"system%285m=20%2C5n=15%29\"\r\n" );
document.write( "\r\n" );
document.write( "And finally:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28m=4%2Cn=3%29\"\r\n" );
document.write( "\r\n" );
document.write( "---------------\r\n" );
document.write( "\r\n" );
document.write( "Checking\r\n" );
document.write( "\r\n" );
document.write( "\"system%28mx-y=23%2Cnx%2By=12%29\"\r\n" );
document.write( "\r\n" );
document.write( "becomes:\r\n" );
document.write( "\r\n" );
document.write( "\"system%284x-y=23%2C3x%2By=12%29\"\r\n" );
document.write( "\r\n" );
document.write( "Adding the two equations to eliminate y\r\n" );
document.write( "\r\n" );
document.write( "\"7x=35\"\r\n" );
document.write( "\"x=5\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting 5 for x in 4x-y=23:\r\n" );
document.write( "\r\n" );
document.write( "   4x-y=23\r\n" );
document.write( "4(5)-y = 23\r\n" );
document.write( "  20-y = 23\r\n" );
document.write( "    -y = 3\r\n" );
document.write( "     y = -3\r\n" );
document.write( "\r\n" );
document.write( "(x,y) = (5,-3)\r\n" );
document.write( "\r\n" );
document.write( "So it's correct.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );