Question 418999
Let the tens digit = {{{a}}}
Let the units digit = {{{b}}}
given:
(1) {{{a + b = 13}}}
(2) {{{10a +  b = 7b + 2}}}
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(2) {{{10a - 6b = 2}}}
Multiply both sides of (1) by {{{6}}}
and add the equations
(2) {{{10a - 6b = 2}}}
(1) {{{6a + 6b = 78}}}
{{{ 16a = 80 }}}
{{{a = 5}}}
and, since
{{{a + b = 13}}}
{{{b = 13 - 5}}}
{{{b = 8}}}
The number is 58
check:
(2) {{{10a +  b = 7b + 2}}}
{{{10*5 + 8 = 7*8 + 2}}}
{{{58 = 58}}}
OK