Question 1031450
Let the 2 digits be:
{{{ u }}} for the units digit
{{{ t }}} for the tens digit
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(1) {{{ u + t = 15 }}}
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The VALUE of the original number
is: {{{ 10t + u }}}
When you interchange the digits, the
VALUE of the new number becomes:
{{{ 10*u + t }}}
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(2) {{{ 10u + t - 10t - u = -9 }}}
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(2) {{{ 9u - 9t = -9 }}}
(2) {{{ u - t = -1 }}}
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Add (1) and (2)
(2) {{{ u - t = -1 }}}
(1) {{{ u + t = 15 }}}
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{{{ 2u = 14 }}}
{{{ u = 7 }}}
and
(2) {{{ u - t = -1 }}}
(2) {{{ 7 - t = -1 }}} 
(2) {{{ t = 8 }}}
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The original number is 87
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check answer:
The sum of the digits of a two-digit number is 15
{{{ 8 + 7 = 15 }}}
OK
If the digits are interchanged the new number 
minus the original number is equal to -9
{{{ 78 - 87 = -9 }}}
{{{ -9 = -9 }}}
OK