document.write( "Question 262900: The sum of the digits of a certain two-digit number is 7.Reversing the digits increases the number by 9.What is the number? Write and solve linear systems of equation for these problems. \n" ); document.write( "
Algebra.Com's Answer #193664 by ankor@dixie-net.com(22740)\"\" \"About 
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let x = the 10's digit
\n" ); document.write( "let y = the units
\n" ); document.write( "then
\n" ); document.write( "10x + y = \"the two digit number\"
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "The sum of the digits of a certain two-digit number is 7.
\n" ); document.write( "x + y = 7
\n" ); document.write( ":
\n" ); document.write( "reversing the digits increases the number by 9.
\n" ); document.write( "10y + x = 10x + y + 9
\n" ); document.write( "10y - y = 10x - x + 9
\n" ); document.write( "9y = 9x + 9
\n" ); document.write( "Simplify, divide by 9
\n" ); document.write( "y = x + 1
\n" ); document.write( "We can arrange it like this, add to the 1st equation
\n" ); document.write( "-x + y = 1
\n" ); document.write( "+x + y = 7
\n" ); document.write( "--------------addition eliminates x find y
\n" ); document.write( "2y = 8
\n" ); document.write( "y = 4
\n" ); document.write( "then, obviously
\n" ); document.write( "x = 3
\n" ); document.write( ":
\n" ); document.write( "34 is the number
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\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "reversing the digits increases the number by 9.
\n" ); document.write( "43 = 34 + 9\r
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