Question 695813
Call the tens digit of the number {{{ a }}}
Call the units digit of the number {{{ b }}}
given:
(1) {{{ a + b = 14 }}}
(2) {{{ 10a + b + 4 = 7b }}}
( note that "the number" is actually {{{ 10a + b }}} )
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(2) {{{ 10a - 6b = -4 }}}
Multiply both sides of (1) by {{{ 6 }}}, , and 
add the equations
(1) {{{ 6a + 6b = 84 }}} 
(2) {{{ 10a - 6b = -4 }}}
{{{ 16a = 80 }}}
{{{ a = 5 }}}
and, since
(1) {{{ a + b = 14 }}}
(1) {{{ 5 + b = 14 }}}
(1) {{{ b = 9 }}}
The number is 59
check:
(2) {{{ 10a + b + 4 = 7b }}}
(2) {{{ 10*5 + 9 + 4 = 7*9 }}}
(2) {{{ 50 + 9 + 4 = 63 }}}
(2) {{{ 63 = 63 }}}
OK