document.write( "Question 266797: the larger of two negative numbers is five more than the smaller. if the square of the larger number is increased by 27, the result is the smaller number multiplied by-7. find the numbers \n" ); document.write( "

Algebra.Com's Answer #195961 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
From above we get the following:
\n" ); document.write( "(i) $\"x+=+5+%2B+y\"$
\n" ); document.write( "(ii) $\"x%5E2+%2B+27+=+-7y\"$
\n" ); document.write( "substitute (i) into (ii) to get
\n" ); document.write( "(iii) $\"%285%2By%29%5E2+%2B+27+=+-7y\"$
\n" ); document.write( "expand to get
\n" ); document.write( "(iv) $\"y%5E2+%2B+10y+%2B+25+%2B+27+=+-7y\"$
\n" ); document.write( "combine like terms and set = 0 to get
\n" ); document.write( "(v) $\"y%5E2+%2B+17y+%2B+52+=+0\"$
\n" ); document.write( "factoring, we get
\n" ); document.write( "(vi) $\"%28y%2B13%29%28y%2B4%29+=+0\"$
\n" ); document.write( "and solving for y, we get
\n" ); document.write( " y = -13 or y= -4
\n" ); document.write( "our two possible answers are:
\n" ); document.write( "(-8,-13) and (1,-4)
\n" ); document.write( "but we can't use the second. \n" ); document.write( "

\n" );