document.write( "Question 186853: a two-digit number is equal to 7 times the units digit. if 18 is added to the number, its digits are reversed. find the number. \n" ); document.write( "
Algebra.Com's Answer #140066 by ptaylor(2198)![]() ![]() You can put this solution on YOUR website! Let 10x+y=the two digit number \n" ); document.write( "Then 10x+y=7y subtract 7y from each side \n" ); document.write( "10x+y-7y=7y-7y collect like terms \n" ); document.write( "10x-6y=0-------------------------------------eq1 \n" ); document.write( "and \n" ); document.write( "10x+y+18=10y+x subtract 10x+y from each side \n" ); document.write( "10x-10x+y-y+18=10y-y+x-10x collect like terms \n" ); document.write( "18=9y-9x or \n" ); document.write( "-9x+9y=18 divide eacn term by 9 \n" ); document.write( "-x+y=2-----------------------------------eq2\r \n" ); document.write( "\n" ); document.write( "multiply eq2 by 10 and then add it to eq1 and we get \n" ); document.write( "4y=20 divide each side by 4 \n" ); document.write( "y=5 -----------------------------------------the units digit \n" ); document.write( "substitute y=5 into eq2: \n" ); document.write( "-x+5=2 subtract 5 from each side \n" ); document.write( "-x+5-5=2-5 collect like terms \n" ); document.write( "x=3 -------------------------------------------tens digit \n" ); document.write( "The number is \n" ); document.write( "10*3+5=35\r \n" ); document.write( "\n" ); document.write( "CK \n" ); document.write( "35=7*5 \n" ); document.write( "35=35 \n" ); document.write( "Also \n" ); document.write( "35+18=53 \n" ); document.write( "digits are reversed\r \n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |